ࡱ> 9;678E@ bjbj " ow   FHFHFH8~HjIÒh:J:tJ"JJJuKuKuKĐĐĐĐĐĐ$+R}` `OqKuK`O`OJJ}WWW`O8J JW`OWWW$X ĉJ.J VkFHS0|(0Ò ݖHWvݖPĉĉJݖ uKMLWL|cMuKuKuK:?D W(?CLRES 2020, Lab 2 Tuesday 1pm-5pm, July 19, 2004 GSCC 126 Instructors: Joyce Chang, PhD Doris Rubio, PhD Maria Mor, PhD Teaching Assistants: Fiona Callaghan MA MS Bill Clark David Corcoran Vinay Mehta Goals for Lab 2 Normal Distribution. Confidence interval for the sample mean, known standard deviation of the population. t-distribution. Confidence interval for the sample mean, unknown standard deviation of the population. Confidence interval for the estimate of the variance One-sample t-tests. Instructions How to follow this lab sheet. Whenever you see a check-mark  that means that you are required to perform some action. Whenever some words are in this font it means that this is a command that you should type in the command window of STATA. And whenever you see an > it refers to going to a series of drop-down windows, as in All Programs>Mathematics>STATA. There are generally two ways to do most things in STATA: using commands that you type in the command window, or using drop-down menus, as in SPSS. Whenever possible, we will give you both ways of doing things in STATA, but you are only required to do it the way you feel most comfortable. On the back of this handout are some questions that you are required to fill in. The questions that you have to answer to get credit for this lab are enclosed in a box like this. You will answer these questions as you go through the lab and hand them in at the end for credit, so remember to write your name on them! If you experience trouble at any time, just raise your hand to let a TA or an instructor know that your need help. Lets get started! Getting Started First we will log on to the computer. To do this you will need your University of Pittsburgh user id and your password. You should see a space on the screen to enter your user id. Type it in and press return. Now enter your password and press return. You should now be logged on to the computer. We will open a folder in which to save our work, and then we will open STATA and enter a data set into STATA. Right-click somewhere on the desktop and select New Directory. Name your folder Lab2, or some other name that makes sense to you. We will save all our work in this folder. Go to the web page: http://www.pitt.edu/~changj/CLRES2020/main.html Scroll down to find the data sets and right-click on calcium.dta and select Save Link As and save the file in /scratch/username/Desktop/Lab2. To do this, double click on Desktop and then Lab2 in the main window (you should only have to do this once; the computer will remember where you are saving your files later on). Click Save. The username is your University of Pittsburgh email id (the part of your University of Pittsburgh email address that comes before the @ e.g. fmc2 is the id from the email address  HYPERLINK "mailto:fmc2@pitt.edu" fmc2@pitt.edu). Now open STATA. Go to the programs icon on the bottom left of your screen (this is the Start Applications menu) and click. Go to the menu Mathematics>STATA. Click on STATA and STATA should start up. We wish to tell the STATA to save anything we do from now on in our Lab2 file. To do this, in the command window type: cd /scratch/username/Desktop/Lab2. Open a log file to save your computer session. To start a log file called logLab2, type log using logLab2.log and press return, or use the drop-down menus. Type use calcium in the command window, and press return. You can also enter your data using a drop down window. Go to File>Open and select the calcium.dta data set and click Open. Your data set should now be in STATA. You should see some words in the Variables window treatment, begin, end and decrease. Click on the Data Editor button (or type edit in the command window). You should see 4 columns of numbers and some labels at the top of those columns. Click on the red button with the white cross at the top right of the screen  to get rid of the Data Editor window. If your data does not look right, ask a TA for help. About the Data Does increasing calcium intake reduce blood pressure? Observational studies suggest that there is a link, and that it is strongest in African-American men. Twenty-one African-American men participated in an experiment to test this hypothesis. Ten of the men took a calcium supplement for 12 weeks while the remaining 11 men received a placebo. Researchers measured the blood pressure of each subject before and after the 12-week period. The experiment was double-blind. Datafile Name: Calcium Reference: Moore, David S., and George P. McCabe (1989). Introduction to the Practice of Statistics. Original source: Lyle, Roseann M., et al., "Blood pressure and metabolic effects of calcium supplementation in normotensive white and black men," JAMA, 257(1987), pp. 1772-1776, Authorization: contact authors Description: Results of a randomized comparative experiment to investigate the effect of calcium on blood pressure in African-American men. A treatment group of 10 men received a calcium supplement for 12 weeks, and a control group of 11 men received a placebo during the same period. All subjects had their blood pressure tested before and after the 12-week period. Number of cases: 21 Variable Names: Treatment: Whether subject received calcium or placebo Begin: seated systolic blood pressure before treatment End: seated systolic blood pressure after treatment Decrease: Decrease in blood pressure (Begin - End) The Normal Distribution Much of the introductory statistics that we learn in this course is based on the assumption that the underlying data is distributed normally. Usually data sets give us data that is not perfectly symmetrical or normal but are close enough to the ideal for our purposes. Assuming normality of our data allows us to make comparisons with populations that we know are normally distributed. Type the command hist begin, normal bin(6) and press return. This is a histogram of the variable begin but with a normal plot printed over the graph. This helps us to compare the data to a normal distribution with the same mean and standard deviation. Type summarize begin and press return. Question 1: What is the mean and standard deviation of begin ? Question 2: Does the distribution of begin look normally distributed? (We will assume that the population that this data comes from is normally distributed with the same mean and standard deviation as our sample for the rest of the lab). You should find that the mean and standard deviation for begin is 114.048 and 9.708 (rounded), respectively. If we assume that the overall beginning blood pressure for the total population of African-American males is distributed normally with mean 114.048 and standard deviation 9.708, we can make inferences about African-American male blood pressure for subjects outside our study. Below are some worked examples. Example 1 What is the probability that a subject in the population would have a blood pressure less than 110? We want to find P(X < 110). Firstly we convert our x-value into a z-value: z = (110-114.048)/9.708. We can do this using STATA: Type display (110-114.048)/9.708 and press return. The answer is -0.417. The area (probability) that we are trying to find is highlighted below:  To find P(Z<-0.417) we type display norm(-0.417) and press enter. The answer is 0.338. Note that STATA is calculating the cumulative density function of the standard normal i.e. (-0.417) = P(Z<-0.417) = 0.338. Example 2 What is the probability that a subject in the population would have a blood pressure above 120? We wish to find P(X > 120). Firstly, we want to convert our x value to a z-score: z = (120-114.048)/9.708. We could do this on the calculator or we could do it using STATA. Type display (120-114.048)/9.708 and press return. The answer is displayed on the screen. The answer is z = 0.6131026. The area (probability) that we are trying to find is highlighted below in green:  Next, we would like to know what the probability of getting greater than 0.6131 is using a standard normal distribution (a normal distribution with mean 0 and standard deviation 1). STATA will tell us what the probability of getting LESS than z is, so we must take this probability away from 1 i.e. P(z > 0.6131) = 1- P(z < 0.6131). Type display 1-norm(0.6131) and press return. This should give the answer 0.27. So the answer is 27% or 0.27. Example 3 What is the probability that a subject has a blood pressure between 105 and 120? Calculate the z-scores: Type display (105-114.048)/9.708 and press return. Type display (120-114.048)/9.708 and press return The z-scores should be -0.932 and 0.613, (rounded). The area (probability) that we are trying to calculate is highlighted below:  Type display norm(0.613)-norm(-0.932) to get P(z<0.613)-P(z<-0.932). The answer is 0.5544. Question 3: What is the probability of a subject having a blood pressure of LESS than 100? Sketch a normal curve and shade in the area of the curve you are calculating. Question 4: What is the probability of a subject having a blood pressure BETWEEN 120 and 140? Sketch a normal curve and shade in the area of the curve you are calculating. Question 5: What is the probability of having a blood pressure MORE than 130 OR LESS than 80? Sketch a normal curve and shade in the area of the curve you are calculating. Question 6: Suppose you are about to start a new clinical trial that is a follow-up to this study. Your lab assistant has taken the blood pressure of a potential subject for your new study but the assistant has lost the information telling you whether this subject was male or African American. The subjects blood pressure was recorded as 133. How unusual is this persons blood pressure if we assume for a moment that the subject is taken from the same population as the first study i.e. Find P(X>133)? Given your answer, do you think this person was in fact selected from the same African-American male population as the first study? Is it possible to say for sure? So far, we have given STATA a z-score and asked it to give us the corresponding probability less than that number e.g. P(Z < 1.6) = ?. We can also input into STATA a probability value, or percentile, and STATA will calculate the z score that corresponds to that number i.e. P(Z < ?) = 0.95. In class we have written the pth percentile as zp. These values are sometimes called critical values. So for example, the 95th percentile of the standard normal distribution is z0.95 =1.645. Suppose we wish to find the 95% percentile of a normal distribution with mean of 114.048 and standard deviation of 9.708. Type display invnorm(0.95) and press enter. This should give you the value 1.6448536. That means that for a standard normal distribution (mean = 0, sd = 1) P(Z < 1.64485) = 0.95. In other notation, z0.95 = 1.64485. We find the X-value that corresponds to this Z-value by solving the following: 1.64485 = (X 114.048)/9.708 ! X = (1.64485 9.708) + 114.048. Type display (1.64485*9.708) + 114.048 and press enter. You should get the value 130.0162. Only 5% of people in our population should have a blood pressure greater than 130.0162, if our data is representative of the population. So we have P(X > 130.0162) = 0.05 and we also have P(X < 130.0162) = 0.95. Question 7: Calculate the 99th percentile of the standard normal distribution z0.99 Question 8: What value of x do 1% of males in this population have a blood pressure equal to or greater than? i.e. Find the ? in P(X < ?) = 0.99. Sketch a normal curve and plot the X-value that you found and shade in the area that corresponds to the highest 1% of blood pressures. Question 9: Suppose you define anyone with a blood pressure in the top 1% as having an unusually high blood pressure for people in this population. Is the reading for the unidentified subject who got 133 now considered unusual? Note: The probability cut-off point that we choose to decide whether some data is unusual or not is often called the alpha level. The alpha level in Question 8 was 1%, or  = 0.01. Confidence Intervals No matter how well a study has been carried out or how carefully the data has been collected, there will always be some uncertainty as to how accurate our conclusions are. This is simply due to the fact that we have taken a sample of subjects, rather than recording results for every possible subject in our entire population. What statistics can do is try to quantify how much error is in our estimates, so that we at least have some idea of how accurate our results are. The most common estimate that we are interested in is the mean of our sample. We would often like to know what the sample mean is AND a range of plausible values that we are fairly sure the real (true) population mean is between. This is a confidence interval. First we have to decide how confident we want to be that the true mean lies between these values. A common figure is 95%, although we can also calculate 99%, 90% or 96.4% confidence intervals if we like. Usually the higher the confidence level the better, but we must balance this against the fact that the more confident that we want to be about our interval, the wider the interval will be. We will learn about three types of confidence interval, and all need to assume that our data is normally distributed in order to be valid. Calculating a confidence interval if we know the population s standard deviation . If we know the standard deviation of the population (from previous research) then the formula for the confidence interval for the sample mean is: Sample Mean z1-/2(/"n) Example Suppose we know the standard deviation of blood pressure in the population of normotensive African-American males is 10 and we know that the population is normally distributed. Calculate a 95% confidence interval for our sample mean. We know that  = 10, n = 21, sample mean = 114.048, confidence = 0.95. Therefore our  = 0.05 because the alpha level is always 1-confidence level. Now, 1-/2 = 1-(0.05/2) = 1-0.025 = 0.975. So we need to find z0.975. Using STATA, Type display 1-(0.05/2) to get 1-/2 = 0.975. Type display invnorm(0.975) You should find that z0.975 = 1.96. Now we can put all this information into the formula and calculate the confidence interval: Type display 114.048+1.96*(10/sqrt(21)) and press enter, and then type display 114.048-1.96*(10/sqrt(21)). Your 95% confidence interval is (109.77, 118.33). Question 10: Often IQ tests and other standardized tests are designed to have a known standard deviation. Suppose we give an IQ test to 25 students and they have a mean of 115.4. The test is known to produce a standard deviation of 15. What is the 95% confidence interval for our sample mean? Question 11: The population mean for this IQ test is 100. Do you think there is any evidence from the confidence interval that suggests that these students have a higher mean IQ than the general population? Explain. STATA does not have an easy way to calculate this confidence interval. It is uncommon to know for sure what a populations standard deviation is, so this formula does not get used much (even though it produces more accurate confidence intervals). We use another formula to work out the confidence interval when we do NOT have prior knowledge about the population standard deviation. To calculate the confidence interval in this case, we use the sample standard deviation s, and we use the T-distribution, rather than the normal distribution (so we talk of t-values rather than z-values). The t-distribution The t-distribution looks very similar to the normal distribution, but it is usually flatter and has thicker tails. The t-distributions we are going to use, all have a mean of 0 and are symmetrical around 0, just like the standard normal distribution. Also, just as there are many normal distributions depending on which mean and standard deviation we specify, there are also many different t-distributions depending on the degrees of freedom (df) we select. Normal distributions have 2 parameters (mean and sd) which determine the center and the shape of the distribution, but the t-distribution only has one parameter (df) that determines the shape only. Otherwise, we use the t-distribution in a very similar way to the normal distribution. The degrees of freedom do not have an intuitive interpretation, like the mean and standard deviation do for the normal distribution. However, for our purposes, the df is usually related to how many observations we have in our sample, n.  Suppose we want to calculate the 95% percentile of the t distribution with 7 degrees of freedom. We denote this t0.95(7) ; this is similar notation to the z for the normal distribution. STATA does not give us the percentile directly: Type display invttail(7,0.95) and press enter. You should get about -1.89. This is the value where 5% of the area of the graph is below this value and 95% is above it (see the shaded region in the graph below).  To get the 95% percentile, we just take 1.89 = t0.95(7), because the graph is symmetrical. Or we could type: display invttail(7, 0.05) Either way, we still get the value where 95% of graph is less than that point, and 5% is greater.  Question 12: What is the 0.975th percentile of the t distribution with 2 degrees of freedom? i.e. find = t0.975(2) Question 13: What is the 0.975th percentile of the t distribution with 1000 degrees of freedom? i.e. find = t0.975(1000) Note: As the degrees of freedom gets large, the t-distribution becomes closer and closer to a standard normal distribution (which is why t0.975(1000) is very close to z0.975 = 1.96). Calculating a confidence interval when the population standard deviation is unknown. If it is possible to know the sd of the population, then it is better to use the formula for a confidence interval based on normal percentiles, because we will get a narrower confidence interval. But if we do not know the population sd then we have to estimate the sd from our sample using the sample standard deviation. The formula for the confidence interval in this case is: Sample mean t1-/2(n-1)(s/"n) The degrees of freedom for the t-distribution = the number of observations -1, and  s is the sample standard deviation. Example Find the 90% confidence interval for the sample mean for the initial blood pressure of the subjects in the calcium study. We know n=21, s= 9.708, sample mean = 114.048. Therefore, the  level is 0.10 and the df = 20-1 = 20. Type display 1-(0.1/2) which tells us that we want to find the 95% percentile. Type display invttail(20, 0.05) to get the value of t0.95(20) = 1.725 Type display 114.048+1.725*9.708/sqrt(20) and then display 114.048-1.725*9.708/sqrt(20) Your confidence interval is (110.3, 117.8). There is an easier way in STATA to calculate this confidence interval! Type ci begin, level(90) or you could also use the drop-down menus Statistics>Summaries, tables, & tests>Summary Statistics>Confidence Intervals. Type begin in the variable box and select the confidence level from the Confidence Level box. Suppose you know your data has a sample mean of 114.048 and a sample standard deviation of 9.708, and 21 observations. Then we could type: cii 21 114.048 9.708 and this would also give us a confidence interval. We could also go to Statistics>Summaries, tables, & tests>Summary Statistics>Normal CI calculator and enter in our information to get the same result. The confidence interval should be very similar to the one you calculated previously (any difference is due to the fact that we have rounded our mean and sd). Note that when STATA gives you the option of Normal Variables in Statistics>Summaries, tables, & tests>Summary Statistics>Confidence Intervals, you want that box to be checked, because we are assuming that our data is normally distributed. It is NOT the same as calculating a confidence interval with standard normal percentiles z, like we did before. Also, Statistics>Summaries, tables, & tests>Summary Statistics>Normal CI calculator uses the same formula as Statistics>Summaries, tables, & tests>Summary Statistics>Confidence Intervals and they calculate the same thing, they just ask for slightly different information. To repeat, this does NOT calculate the confidence intervals we did in the previous section, because it requires you to enter the sample standard deviation, not the population standard deviation, and so it does not use z (percentiles based on the normal distribution); both these STATA methods use t1-/2(n-1) values instead. If we want to calculate confidence intervals separately for the calcium group and the Placebo group then we can do the following: Type bysort treatment : ci begin, level(90) and you can also use Statistics>Summaries, tables, & tests>Summary Statistics>Confidence Intervals and click on by/if/in and check the box for repeat command for groups defined by and type treatment. Question 14: What is the 99% confidence interval for the decrease? Question 15: What is the 99% confidence interval for the decrease for each treatment group separately? Question 16: Do any of these confidence intervals include the value 0 in their range of values? Why might this be of interest to us? Question 17: Do the confidence intervals for each treatment group over-lap much (have values in common)? Why might this be of interest to us? Confidence interval for the sample variance So far, we have found two ways to calculate a confidence interval for the sample mean. We can also calculate a confidence interval for the sample standard deviation. We use another continuous distribution called the Chi-squared Distribution. It also has one parameter (degrees of freedom), like the t-distribution, but it is NOT symmetrical. A Chi-squared distribution with, say, 10 degrees of freedom is denoted (2(10). Here is an example of the Chi-Squared Distribution:  We can find percentiles of the Chi-squared distribution. The 90% percentile of the Chi-squared distribution with 7 degrees of freedom is denoted (20.90(7). We can find this using STATA: Type display invchi2(7,0.90) and press enter. You should get a value of 12.017. So 90% of the graph is less than this point. See the diagram below.  The formula for the confidence interval for the sample variance is: Upper Limit = (n-1)s2/(2/2(n-1) Lower Limit = (n-1) )s2/(21-/2(n-1) Example Calculate the 95% confidence interval for the sample variance of the variable  begin . We know s2 = 9.7082 = 94.245 and n = 21, so df = n-1 = 20, and  = 0.05. We need to find the percentiles of the Chi-squared distribution. Type display invchi2(20, 1-0.05/2) and display invchi2(20, 0.05/2) which should give us the values 34.17 and 9.59. Type display 20*94.245/34.17 and display 20*94.245/9.59 which should give values of 55.16 and 196.55. This is our confidence interval. To find the confidence interval for the standard deviation, you just take the square root of both values. There is no single command in STATA (that I could find) that gives the confidence interval for the variance (or standard deviation). Question 18: What is the 90% confidence interval for the sample variance of the decrease variable? One Sample t-test (one-sided and two-sided) We may want to investigate whether the mean that we calculate from our sample is significantly different to some known benchmark or some number of special interest. The men in this study are described as normotensive, meaning that they their blood pressure is normal to begin with. Suppose that we wanted to verify that this was true and we defined elevated blood pressure as any value above 120. We would like to perform a test to compare the mean blood pressure of our sample against 120. So we will assume that our mean is less than or equal to 120, and try and gather evidence to disprove this hypothesis. The notation for the two competing hypotheses is given below: Ho:  d" 120 versus Ha:  > 120  Ho is called the  null hypothesis and in this case is Our population mean is less than or equal to 120. Ha is called the alternative hypothesis and in this case is The population mean is greater than 120. The point of the test is to decide between these two alternatives. We will perform what is called a one-sided test, because the alternative hypothesis has an inequality only going in one direction. You will learn more about t-tests in class, but for now you need to know that we calculate a t value from our data (called a t-statistic) and then we compare it to the appropriate t-distribution to see how unusual the value is. We do this by calculating what the probability is of observing that t-statistic or something even more extreme, if we assume the null hypothesis. This probability value is called the p-value. We also decide on an  level to compare our p-value to, in order to decide whether it small enough to be considered to come from an  unusual event. If our p-value is less than , then we say that we  reject the null hypothesis. If our p-value is larger (or equal to) the  !+01:Ghiwx      / A B C D S _ 庳 h^^J hD2o^J h2 ^J hf}^J h@z^J hb^J h^J hFC^Jhs h h; h h h hBN^J h ^Jh h 5>*^Jh h\Z^Jh h ^J hBN^J hJ^J hs^J01:GXixC S L gdtkgdtk & Fgd\Z & Fgdgd $a$gdBN$a$gd gd\Zm  > ? ZZ^[89:GH]ڠړڄڄvfv[vhhtk0J^JjhhtkU^JjhtkU^JhBN hBN^JhU/htk^J hv^J hhtkh_1thtk6^Jh Hhtk^Jh HhtkOJQJ^JhPe4htkOJQJ^Jjh7h@U^J htk^J h htkhtkh h\Z^J hb^J hoY^J# G H Zj=KtXgd5sgd5s & Fgd5s & Fgdtk & Fgdtkgdtk&$d%d&d'dNOPQgdtkgdtk]a$(0=AFy:Z 9c&7Dsķ~zh_h>0h5s^J hsFGG n o gdN & Fgd_ & F7$8$H$gd_gd_gd@ & Fdd[$\$gd>0 & Fdd[$\$gd5sgd5sX]pqrE F G L V [ n !4!M!!!!!!K"_"E###### $$<$ij{wsksgcgcgc_ghlhWah* hNh_6h_hNhNhN^J h ^JhNOJQJ^J hN^Jh_5OJQJ^Jh_`h_5OJQJ^J h_5CJOJQJ\^JaJ h \^J h_\^Jh_OJQJ\^Jh_5OJQJ\^Jh(Mh_5OJQJ\^J h_^J#o !!E#O###7$$$$$&&l'n'f(( & Fgd_gd_ & Fgdh gdl & Fgd* gd* gd* gd_gdN&$d%d&d'dNOPQgdN<$E$H$X$y$$$$$$$$$$&&&&&&'''''k(((((((((3)4)5)ɿzqjbj:h_U h~cgh_hoh_^J h7O:^J h^J h_^Jh_OJQJ^Jhh_h*  hh hh  h~^J hN^JhNOJQJ^Jhh OJQJ^Jhh hlj/hwBU hlh*  hWa^J hl^JhWaOJQJ^Jh* OJQJ^J$((2)3)5)6)**P+Q+i+,,Q,S,T,U,,,^- ..&$d%d&d'dNOPQgd  & F gd_gd_ & Fgd_gd_5)6)e*f*g*h*x*y*z*{******(+E+F+M+n+x+y+z++++++++++2,O,Q,R,Z,y,z,,ĹīϜ߆{mih#~h%Oh_5OJQJ^Jh#~5OJQJ^Jj-0h;Uh^hwB5OJQJ^JhwB5OJQJ^Jhh^h_5OJQJ^JhP"5OJQJ^Jh#+5OJQJ^JhwBh#+hP"h* h_h_OJQJ^J h7O:^J h_^J hoh_',,,,,--^-h--- . ....}/000000;1\1]1^1222222223373;3<3B3C3w3333 44i4ɽɹzhZYhZY^J hZY^JhZYOJQJ^JhZYh hH*hMh] 6h] h H*h h H*h hyhJhkQh68h hw(hN hw(^J hy^J h_^J hN^J h^h_h_h0.]1^1334V8W889::<><>>8B:Bgddgd@gd&$d%d&d'dNOPQgdp0 & F gdZYgd &$d%d&d'dNOPQgd68i44444444666R6b66677 8,8T8U8V8W8a8t8v8888888888889 999Ƽ|xtpxtxlxtxthw(h;VhIh7O:h?h?H* h?H*h?h?H*h?hh h hQ hk^J hr^J hp0^J h(b^Jh(bOJQJ^Jh{(h{(OJQJ^Jh{(OJQJ^J h{(^JhQh{( hZYH*hZY hZY^J h^J(9!9*9.91969798999A9M99999999d:g:x::::::1;7;=;I;J;R;S;a;d;<<<<<<><f>>ʾʵ~zvrhQUyh%6?hd hhhtOJQJ^Jh(=htOJQJ^Jh%h7hththt^Jhh2\]^JhFCh|^uh IhBhhh1 h{"shh8)h h^Jh7O:h{hbW^hTk+>>>~?????????@@@@6A7AtAyAAAAAAAA6BBDDD D$D(D*D.D0D2D:DD@DNDDDD8E>EEBFFFFļĸܴܴhhJ'h"Kh h"K^JhADhADH*OJQJ^J hADH* hAD^JhADhh_vhe9,h#h#h]/h]/6hKh3hh]/hW [h@h"Yh@2hUh =hdh4:BBD>D@DPD&F(FGGZHHHII8J:JlJmJgd7gdx & Fgd AgdgdM & Fgd"K & Fgdygd"Kgd"K$a$gdADgd]/gd]/FFFFFFFG(GbGdGnGGGGGGGH.H@HBHXHZHdHHHHHHHHHbIIIIIÿyrlfl`l hM^J h^J h A^J h"KH*^J h"KhM hMh"Kh"cOJQJ^Jh"KOJQJ^J hyhyhyhyOJQJ^J hy^JhyOJQJ^JhyhM h"KH*hq>h(=hQBOJQJ^JhQBh{h Ah(=h"KOJQJ^Jh"K h"K^J%IIJJ5J7J8J9J:J?JGJlJmJvJxJyJJJ]KKKKKLhLrLsLLLMmMMMMMM4NMNNNONQNaNoNN{sn{ h6hc*hc*6hhc*6hc* h^J h P^J h_^Jhh>C6^J h@^J h>C^J h3#\^J h^J hZ^J hJ'^J hG^J h7^Jhxhx^Jh7OJQJ^Jh=yOJQJ^J h A^Jh AOJQJ^J+mJKsLtLNNNRRRRTTUU)V+VVVVV & Fgd0  & FgddegddegdRgdQCgd7&$d%d&d'dNOPQgdZNNNNNNNNNNNNNNNNN;OSTɽᨢ h^J h[B[D[H[`[b[[[[\ \,\T\V\Z]\]]]^^^^^^^^,^c^d^˽ܷzpjp h8X^Jh8XOJQJ^JhQ|OJQJ^Jh8Xh(=hQ|OJQJ^JhQ|hc h9J h9J^JhEhq6^J hZ^J hq^Jhc hc H*OJQJ^J hc H*^J ho^Jho hqNqqqsssttxuyugdBgdqV & FgdHgd^gd^$a$gdB@4$a$gd0XQgdL & FgdPagde9,gde9,n(n7n~nnnnnnnnnnnnnno0oOoPoQoToUoWoXoYo[oxoyo~ooooop pztnhna hLhPa hL^J h ^J hPa^JhPaOJQJ^JhPaCJaJh%fCJaJhPaCJH*aJh%fCJH*aJh%fCJH*aJ jchK h%fCJaJhh%fj=ihK Uhe9,hPahK CJaJhxhK CJH*aJ jchK hK CJaJh_q"hK $ p"p$ppppppppppppppppppqqqqq q"q$q&q,q0qwhLU,Nrnr~rrrrsss"sFs^sfsssstt t6ttttwuxuuuuuv vww(xdyfyhypyrytyvyyyyyyyyyyzzh[bh8H* h4?^J hV}7^Jh8hAhV}7h ha| hz}hc.h ehhB hHhqV hqVhH hHhHhHOJQJ^Jh(TOJQJ^JhqVh_\^ hH^JhHh(T3yuuu vfyhyyyx{y{78GHgdF5 & F gdF5gdV}7$a$gdV}7gda| gdG7gdB&$d%d&d'dNOPQgd ezzzzzzz{{{{{{x{y{{{{||||||"}~~~~ :<>b3468FGHMȾ䖒hU!hU<h-|hiUhS,hiO5^JhS,hiO5hiOhS,h hn^^Jhn^hg^h-hz}hS hS 6hRKh_3h2hV}7hIhAhAhymb4level, then we fail to reject the null hypothesis. The logic behind the test goes something like this: if the p-value is small, this tells us that if we assume the null hypothesis is true then the probability of observing our data is very unlikely. Hence we conclude that there is evidence that null hypothesis is false. Type ttest begin == 120 and press return. This will give you some summary statistics, confidence intervals for the means, and three t-tests corresponding to the three possible alternative hypotheses. The one we are interested in is the one labeled  Ha: mean > 120 . The output in the results window should look like this:  I have circled the part of the output that is of most interest to us. Suppose that we choose  = 0.05 for all the following tests. Question 19: What is the t-statistic and the p-value of this test? Do we reject or fail to reject the null hypothesis? Does the evidence suggest that this group of men have normal or elevated blood pressure? Question 20: Suppose we had Ho:  e" 120 and Ha:  < 120. What is the t-statistic and the p-value of this test? Do we reject or fail to reject the null hypothesis? Does the evidence suggest that this group of men have normal or elevated blood pressure? A two-sided test is when we have something like this: Ho:  = 120 versus Ha:  `" 120 Another way of writing this is: Ho:  = 120 versus Ha:  < 120 or Ha:  > 120 It is called two-sided because we are allowing two possibilities for the alternative hypothesis. We use this kind of hypothesis when we are checking whether the mean is equal to 120, but we are open to the possibility that the sample mean may be greater or less than 120. Question 21: What is the t-statistic and the p-value of this test? Do we reject or fail to reject the null hypothesis? Does the evidence suggest that this group of men have an average blood pressure of 120? The End! Saving the Lab At the end of the session, follow the following procedure so that you can save any files you may want to review later on (e.g. your log file). These are the instructions if you are saving your files onto a floppy disk. If you have a zip disk, just do the same steps but with the "Zip" folder on the Desktop rather than the "Floppy" folder. Insert floppy disk (or zip disk). Right click on the "Floppy" icon on the Desktop and select "Mount". We can now save files onto this disk. If you do not Mount the disk, then your files may not save properly. Close your "Lab2" folder if it is open. Click on the "Lab2" icon on the Desktop and drag the whole folder to the floppy disk icon on your Desktop. You should get a small menu giving you a choice to "Move" or "Copy" the documents. Click on "Copy". Your files should now be on your floppy disk. Double click on the floppy disk icon to check that there is now a "Lab2" folder on your floppy disk. Now close the floppy disk window, and right click on the floppy disk icon and select "Unmount". You must do this in order to take your disk out of these machines and still have your files saved. Now press the button on your computer to eject the floppy disk. It is very important to save a backup on the university computer in case something happens to the disk. Click on the Lab2 folder icon and drag the whole folder to the AFS folder on your desktop. You should get a small menu giving you a choice to "Move" or "Copy" the documents. Click on "Copy". Your files are now stored on the University of Pittsburgh computer system and can be accessed from any computer with an internet connection. See the instructions below on how to access these documents from your home computer. You have finished. Accessing the files from home from the University of Pittsburgh computer system Here are some instructions FYI to help you access your backup copy in case there is some problem with your floppy disk or zip, when you get out of here. To access your backup copies from your home or office (Microsoft Windows!) computer do the following steps: Open Netscape Navigator or Internet Explorer. Type  HYPERLINK "ftp://username@unixs.cis.pitt.edu" ftp://username@unixs.cis.pitt.edu and go to this destination. (eg. Using my username, I would type  HYPERLINK "ftp://fmc2@unixs.cis.pitt.edu" ftp://fmc2@unixs.cis.pitt.edu ). After a few seconds, Internet Explorer will ask you for your University of Pittsburgh username and password. Enter these and press return. After the screen has loaded, you should see a list of files and one of them should be your Lab2M_q @Pn|(*,@B<>{rkg_g[hT\ hP hP 6hP h$h>$OJQJ^Jh(=hF49OJQJ^JhF49hW^hEVhZh$jhZU hF5^J hF5hF5h5vYh4?^J h4?^J hU!^Jh,hU!OJQJ^J# "*,>@~ gdb0gd $a$gdP gdEE`gdHJLNnprtv~ 43rstv~u¾h. OJQJ^Jh,8OJQJ^J!h}hjTB*OJQJ^JphhjTOJQJ^Jh}hjTOJQJ^JhjT hEE`hP h Vd^JhG7hc^J hL^J hc^J h^J hb0^J h ^J hP ^JhP 3tvLPbus & FgdjTgdjTgdjT & FgdjTgdjT gdjTgdEE`gdb0&$d%d&d'dNOPQgdc-.KLOPVdbptu0ŷũ͋vvvdVhjTOJQJ^JmHsH#jhjTOJQJU^JmHsHh#%~hjTmHsHh6OJQJ^Jhj_hjTOJQJ^J h#%~hjTOJQJ^JmHsHh. OJQJ^JmHsHhq(AhjT5>*mHsHhjTmHsHhjTOJQJ^Jh. OJQJ^Jh}hjTOJQJ^J!h}hjTB*OJQJ^Jph012STU$<rsqrsմմմzpnd\XNheHOJQJ^JheHh_mHsHh_^JmHsHUh. ^JmHsHhhjT^JmHsHh#%~hjTmHsH/jhbdhjTOJQJU^JmHsHhjT^JmHsHhjTOJQJ^JmHsH$hbdhjT0JOJQJ^JmHsH#jhjTOJQJU^JmHsH/jhbdhjTOJQJU^JmHsH. Just drag and click that file to wherever you want to put it on your home computer. Close Internet Explorer. Answer Sheet Lab2 CLRES 2020 Summer 04. NAME and DATE: Question 1: Question 2: Question 3: Question 4: Question 5: Question 6: Question 7: Question 8: Question 9: Question 10: Question 11: Question 12: Question 13: Question 14: Question 15: Question 16: Question 17: Question 18: Question 19: Question 20: Question 21: PAGE  PAGE 14 sr&$d%d&d'dNOPQgdzgdzgd_&$d%d&d'dNOPQgdeHgdeHgdeHgdeH & FgdjT +,78CDSTfgrsŽ~umh_mHsHh[hB^J hI^Jh[hI^Jh[hx^Jhv?hBmHsHh[h>b^JhBmHsHhv?hzmHsHhzmHsHh#%~hjTmHsHhv?heHmHsHhheHmHsHh}q>*mHsHheH>*mHsHheHmHsH)gdz&$d%d&d'dNOPQgdz ,-./01234&$d%d&d'dNOPQgdBgdBgd>b45678DEFGTUVWXYZ[\]^_`abcgdBgdI&$d%d&d'dNOPQgdBcdefgstuvgd_gdBgdI&$d%d&d'dNOPQgdB "#019:;GHIJQR^_`aefijmntuvxhm hm0Jjhm0JUh[hG;^Jh[h<f^JhO"mHsH h<f^Jhv?h<fmHsHh<fmHsH h/1^Jhv?h/1mHsHh/1mHsH h_^J hI^Jh_mHsHhv?h_mHsH2gd/1gdBgd_&$d%d&d'dNOPQgd_ gd<fgdBgd/1&$d%d&d'dNOPQgd/1 !"#123456789:;HIJKgd<fgdB&$d%d&d'dNOPQgd<fKLMNOPQR_`abcdefghijklmh^hgdG;gd<fgdB&$d%d&d'dNOPQgd<fmvwxh^hgdG;h]hgd &`#$gdP xyh[hG;^JhAh[(hhmh0JmHnHu hm0Jjhm0JU 1h/ =!"#$%DdT  c 0A W?checkb6uf4sJDn uf4sJPNG  IHDRy0PLTEiX'6tRNS@fbKGDHgIFg>U cmPPJCmp0712OmBIDATc`@PZ*t&ʸ &/hƻ `߫w ^0.%e(Z PE'IENDB`DyK fmc2@pitt.eduyK *mailto:fmc2@pitt.eduDdH  C $A errorb1oqPՏn1oqPՏPNG  IHDRb PLTE^tRNS A cmPPJCmp0712OmEIDATcX55jJU K^1Lhb@ˊa >@eրt>a_@ oIENDB` DdIT  C 0Anormalex1_1bcusUkYƪ?sn7usUkYƪPNG  IHDR'aICsRGBPLTEoTĻIDATx^FQIW[ !cN::=m;}w,gρl8p1 |lp1 |lp1 |lp1 |lp1 |lp>)dy3L&o]>!J?h#UOcgz3z\C`/C Ϗ;4O(&Eg}^ͨ; c1F,>F1Ql8c_Κv -Xz!neY~2Z{ + sS xO(ͤ'Px,$'.S\4Q얼TL˗ja&gɺg9Wᚊ\"4Sj }J < _QL+W2+ E2i-CW"̲Jdhu|\s$%l]^5v0%I -X*5j+T,&MN3ϲ@|4*(Y`r,p),֋j-Wlc~ۼ^B ۝eC 8\ 7}hp+3hO܅;|1{4b|*?{:ܥk] |>^}ˁk}F7}RSm,$AYtX@clji]zu I[׆|ߘC__1">.7%mo`?þ<~7.-ٺ=;j~@܁慨?~#}X3 ~~~܁xP-r^Ĕ܁C68RJ;2q^0q^%3?hv5MxqWVʁG hMwV%]T%3hJ܁n4Qwšnm960SN0t#S7 X 3iG'7xp m5-\i8iQe>G)+\OG?>.\OG/?z? \Q k/ٖytxj_ٟ/CµKĉ\m R5mH!cė- R]gf(tsn^@D5=/1L)o9zx_iNڊ~H:'p!NKթ]Tj}z_|5KK]ʥkފc;NhTxףW,>p;pfD'FhTxߣ)\SGG.kPL)M\y/ *\m p oa*_s^=(6u1%pIkHT. \OGOOɺ \pGUҭ8yݾB. \gGOٯD[I[eQN*x߮wp*V8ң +\Q]-fe.)%H'BTdWf˼>|[:,PhL=5m-X.p:Eͷ\1yv 88pQӧJPa#Yz,/xIx+\SG~/9uppx 9qރ}y8FcN~]GT$ ?/Q5td<!E\F˧oiч(\OG+NÀ+XAhO/nU%q#(VTރ:PG/.%8(c9rZS2Q۲(zf/N0n, >깱R͇'885+ >ΥI^ ӦD݁K~cq/(C0.}g8 Ť uZoP+8 85G_yױ5{/pr>h5} .H2BߔfEiRR$cel§Gk`H ot<%%S^pG+\Q}7W8[k|WV$pB, go4nC~/JD-V ^(7aE(JM? Ng_Lyqv~fil|-q楛g'뀳38潜SORR _GD$N]_Cx޶O~}&kg> dlǗ bfG|ӏ5s*C޳bxx2"=SXIO='eDy |_\FS/^\bG6 ;>~:$\5Ԥ-~N P 4" |nҶƩfY.#- m>q%m.{A M8n8Ug7 \2>:>Bӈ.{ޒ7ggN`l{ÙcVG^ |q^s .Dи=y/VusG^|[|nLE]hn PyzZCLѼlO_Xyf냶vǽ|[V!nxPXy+დ7'V%p֪x=A޺^˺vow-)IR,/]#O{K>FS |Z.WQ`xļ*h.p|O, gX] ++Á+1c(|1>ʊp`aeE}8pE0f Łϰ>"?>ʚnZ٭!2TIENDB`DdIP  C ,Anormalex1bO)aMx4g(+~n#)aMx4g(PNG  IHDR'aICsRGBPLTEoTĻIDATx^( FWK-S ! 61`[饀`!ܟٯ}

֚ fA` f\Sk 7y`3sM|3lf)܀o5~O!8=Iazy QA{uWVIS:v/S冹w=عG~j/ˁ_g.dQu1CG|0pES1aG: ~jnER,nVI539~KSj͓QY!|ZHI 4Q>tm˜v8LoxCvWeXF#׮9&B+|͙z,x1n?)ųW ÜR)qzk. "u͍Μ?Ŀ@ɲ987| !\\ߓ]Yͤ49$a@e)i"(8mZ :&ϢT2`H,0| .8ӰyȌ./<ҞM)~}|Z LCxśb5z@/^A~KXN(t`ipu(<œszcIaYʩCUW6e|2X+DcY )5 Hge YT"KU 󜉫Ԃ*|ue=.ZX R~洖\%|05"JF]#‚uV)vl?]+,ź ]bí/mH@r&UQp5.D/LK7`dؘbEQ ?vb@ P ;% \jeٽy@HM;4I؀gHܥϐd'Kc!Nr\?C.y`<!\/jAδ~vQ3ˀciu<Ӊ=`)]j(tpȠ1xT{OM\G 1oJǏd =|X_Im)={r-WgU\{c:y ޿7džXh;x+ohOW7wq{Kw j^B Q+7%7 7wQ /ֈ~.>g~܀x-rĴ܀C68VBbI3qO1qo xNHjKcZg"BB:CyEv7 8R#hjmgoы!i\bE@{(p7m duLjp7_cR"cMOW2osII܀@Q'qMzOJkw27<@琧۱ÔKqٿIN\YX<=p#pR\qxmuWop&P?bM1ٙ:2 Aj ZgsgE*sr7N Z咥D 9a0kQ8K'3w"Wr^JS;3\9Y#K|O纾/ { _lpuY S8)lʾƊO 7+C|"" Ms +\ɽE4s W*p8B&A*p,vJ}K=t8'\~WyG[¥ߚ!{$梁3 (\ANƫ\2pnpGp8#RJWׁcn?vb8T~}]s`3WlǛ ~H jm8 "e=S"kV8yV8FwT8:l .NGoQ v sK*1(\tN')e*G^쥇Wtp:KN;ekJ|+qBW<"),:pXpT.pҞwDw QŽ qA}wŮ{csK۔.U( lt•"W?_ )? ihV=p9%`^֪ p!u 8}Gqk.pz@mRG?BiKt) _〟)%@ ,EBV"r: x< +pEmG&CC%H\ͱ]W+V+8zEJ:Z `EtI/KM {xBq 1ej'+| x:էmopoGg&gri }kVr9!>7dM iIKxqN<܆T \Nf↛#p§JoDT>8xy_v m8c=9 ez0a ?pҠ+S-Sܭ ^]94;!<pIEO7h=vpbn>)ӢEUO8,'G] lR,/|O"ywd~_/|ZBoMW>o; 3_D}P OI_mU5[TVs.mځϹaK+M蟊fʁ[m S&P/US6fBx>rU1p)$W \oÈ+.a%_#tśGnϭ?rǸǣAj~8Dw.7WJs:xs￐k>Aޮ!Y{n 77W\&o^'݊7EO=13oz'Ky On}+p^E𸒳3+o*=;$?Ixλ`I쒁nSb+_r }1 qŶs$\fUz(6دx%BZp!ӷiP=`Sހ+HzLy{ u1 rpǔ7R=S9#-* ߳L0n}îS_*ccr F'p/mEa7ScNw1###K#GxC CZMawn"mb-nm2{NV$y0L&: z'|V#5}=B>tqH=5\~Î-LINXu$tp%Cfv[} &]B rF5ﱰorr49JՀA!Z_ g^R- R8𺏖jaY5?^Z W7y`Q6Dמ IENDB`DdIP  C ,Anormalex3bq0V)o˕S;aRMq0nE0V)o˕S;aRPNG  IHDR'aICsRGBPLTEoTĻIDATx^ݬ-vp4@~sH֟?>8|{ZO͜,YwM|3 l]Sun7f5,YwM; ] ~ӞNvSwIw=f7 w*te\O^_T 6Ti۹a[zdmpfsV?Gͦ'w}L6 epZJwBۺ \]y'zF+`QfrZ/ds!-X f sS xx_.I:P39x햩M n+LBn1J%|k,Z7.\*aN@}SK`/cJ <^4UQ/=hW)dd2Z:.I?@ҹgLr4nuqLR<{EK._”$^{x*a}2je>}_s9a R]+tpȠ q-pTpnZ7px88) (zxX/$۶pMvH/NPO|=mC^Gymd<>X)i;x_?þ⪼!]354n/_^D cl_!+EveޔZ/z>5<Q x'À O\<0W͓ea,,=/.jo+\?s\ZLosI~ `b:N`od=<~,Lnpa8x[Λo5E-՛˒88i h{oe-"Qmto \qX"?;$8XβGC Po($/!?,x.djRx:,*K.'#I?\OUZfxH^'`&E(EU*^ʏp)sqpI BU?GYLPwvHoSːԀδ2)e mӀϏ8GJ H΁H(:F6hUxKVڜ6EinU?c%HxK*-g(>ը51Vjh"7TcO]ZEu HX&tYI[HܨZ~IM S 3C:F>5oCg|ąvv޾.NXw%gJ /6 8\ssW/ݼZi+f~M/ u^6dOxGߗVd$^.CBx~}!p >> iu^& ClO#W埉k޳pa pcRx,8_2uKMnV @VCHY*iY_xӹs!g \@6-o[8eF7>Qesf++EDE-F3N1pRFۉ]_8RB(c3uys9Sm08'KYx~)<|{Ae\[ 58iW  kη,%84$ 򀏋j-0J[R#m D:[29kܲV\CϚ3s}{XE>h F}_ ٘,=4C?v]{YClH j\^ֿbEާx?beNΖ̕exg z7:<(oignP3J?,=%ޘ p5}Á_.7%jOzwe*z0/UZČ^Ar7M"ذ8ĹMG0E/C [DU,G5x$荢+(+,шtOzB(U#"ȁS-LP'e,N*X=->v{ 8P3ૐDÀ# J1 Id? 8P3ૐDÀ# J1 Id? 8P3q燼 Zg$_d}}zC:jnIZ絆#,` Gi"|%pV*bWGi"|%pV*bWGi"|%πTc0 ,j&V IENDB` Dd J  C &Atdist2bx qz@}u/T FnL qz@}u/PNG  IHDR3F;sRGB PLTE(k IDATx]&i)>E9Ei")0?鎖L_CA/K4K4K4Kj4446ёbbg5|ghئ35,ti|FWjrCnFF) @`1 Ϳ0F0Km4&F60dƼ4bh`˔kO$V&4̩m&o)]^D4̏b6OcABh"M*l|4_>K̞(4ipFMJx\Wil-Gۙ7 haF2I6[]5wxī96i@| $MgؼH6C}@c⑰y@H،kLŊkŸa(6W-QUCxw،jf )6Aw=tFg?fkH|װh fk$5GJ+mp'7َ%T-$ΈHS*axO ќg{F#b@svЏ$%ޣ9?R6_s ~Ua"'kGpWFƋ_ x5c=6E#2W#uF iSSӫy nS#:= N +hGi>MPcfExKvKBէ'kXYçj2"ޥf~*]Y̽#uY#?K#fj¸4mMQ*s4x\'S΁*(f-xAjQϑo[4xI5Z{4'kwE_sݿ<5  lL'Mo_FlwqΛE׿ocF>p:42(Ns5rx4-f5a*/vS4,MK FcpI4ǟG!ywӣGq?ˑ4(!x ʊY8&n#&&qx滦Yy+A4iL8KszkQS\GXoėNgHhln$nͥVpH4i 4L5B?Q{a5Bi~P J.A )ikܚ_vmGB$ץ1V4|HU*{\/N`YIՒٰ5F5Q8k@57n5.uk JAbQ|NyhBOȚ{Eink?4W[Fܚƶo [J4{ՠ2cMǢ--/،Jo'5h_h4k5M 9jwgt׌u3h& rl&1f4`$lF M0f103Fb,I~ǥ25uތcFM؈12] fXوܕ73bH65՛cXgjVwYMͬF#u1cmf6cMƁYidY5ٌ{3+> "Qf<7kF\`fk!ƉEjj513[^͈2nVSGbHЌ+2 4d ͸.943:㎌;3j>++3xL᥅GcydJƌW3OԘnL$NŸ53Vj**ƱDZf,ِʌLf,L6#Y1,5\͘b)KHl1N:SsQfR#`&Tl$+0S@f̔FŌ3eU071Lr5cDM<7&2Dg#JdC<Θ1fHl1q̲۹aZ#z:fʪ5Ob#ͬ--f\tf35d0?IifK`,6˶M^3eIqf\`f,t3L~o1E3Y`3 f0`3 f0`3 f0`3 f0`3 f0`3 f0`3 f0`- f0`3 f0`3 fho{b(31cfv^u5f:K\P.f*GwP[l?fWd| `3 f0``3 f/0,|&Nߞ`~n.A|^닼]'O\~r1ϝʹMɑ>߬Aߵfv6pPplMǮF ̮?:iF{ivN̤mWp)ijC`f̾ݱ>[Ӥn3@#:?w3ʹ:M75@0q`9t|ܦ7~oǽ13erl>'uM!!33333``````B0C0C$c{IENDB`, Dd J  C &Atdist4b  Y'@wnj U]nb Y'@wnPNG  IHDR3FsRGB6PLTEMMMhhh|||(t/v IDATxmc:)쁠+-p?,۳M&2/BB0C0C0C0c+ 6Cg`f.:3 f0`3 f03s f0`3 f03 f0`3! f0`3 f0`3 f0`3 f0`33R3l62(^ fF9L~zȹOQ>1G*):׃479=GXfXrqK8a3_&73 3nFy󿹩(vVb){+oUPJ`&$~emziُU7f0h1:{ fBNE_„ 1*y1Q.ُU7f0ӧ7o? fsC7TEMoKMyNS7zyP\Hq=q<>oKZ3(3 f0`3 f0`3 fU\K`3 "`Fgd03 f0ufܑ f0͌?2 fqQXj0}|3f03ʗ@3lm3n}—m$?3߭fj0˳5̌1 f:?ycL]3 嚌O3L=MGgEL3.X5S1qz2x:q2Xdxw :% #:"F_jL$S KoWE,&Oj̜El1Ac$$>:|q)7E3H!&ϟ,@2ix@c$2K*2G$3cVtbFwS2-OJ&E憧%֌e4۝Lb3ըm&܌Y4Z\L34}R^wR5AL3T39g hiL2ucQsAn9=GsL.4\});=FL573'yx L4O]{zbb^z\މ8qIeX']ҏ4UXkǪیJ&~qJFn+frQ`FcjFn#fm&e%\ wb.2W6L9˱ 5xi:ܤL~3 P>=yRoFT`&S)r .1JXxp)dя&sD5fԫ4Eb4Q&k45VfREF8Mfы&[ԑQg&YeFmLR4#;$[?0o^j&6iz3JŨ5{AFQj&v-݌f2zDE3{ߒ\Un3jKsSL5w+ɨ&Z@)62XC͂]JJ1q&f1bfԂ dl(5c`bM3'fl3nfю2lF1CƔ,ۉ@Ƥ[Kd @&[b YFkbLYf b,YFbkԄXM czY%RabɅjVi1̴3 hgD,1nfѥiƸff:ffYEf37fVV6c3<䭁}1ɺ83źUJo%f~T=f~ֽWKVyqDƭWcʷz 3k޵f 3~7>"3vld 4Ӯ}ҴԌG/1?w4^veffgWfVU3;5.fkf;C1k3/I37Jf03f03 f66`3 f0`3 f0`3 f0`3 f0`3 f0`3 f0`3 f0`3 f0`3 f0`3;>CoGcƔILW/h&fFˣ]w(?^&٩~~yó$3s=#<'v`k3; 3 f0`3Qs>"oaTv۟s>9ܬB*`f/7fr9vL63Tsϟ\틼c36՗c` fUu|v0Lfȯf.e? z-'9t˧ %8!,Ϙ!)u#K*Ő"o!?8SayO~#3̜󥮞9ۇmL".3סbbؼbf}98iE٤o`````B0C0C0C0C0Cfffff QNՌIENDB`DdN P   C ,A chi_graphb] 22hC 9 in1 22hC PNG  IHDR,L PLTE///___???pppOOO```KKii@ --`p0<<p%p`p``Up`P]a`P``PU@?@ 38 " @'TiZZ`,`\h Htpt`JRNEO$_ttXOtQPtP0/]}V(t V(V(%x\g@vut`u0snMtctlv`|(?cIa.m8 <<UUT4 c*J/|4v67(\p"xxuP.@symuHu 7|8""ntoolspcG`x ]\uܥuPv \(icMacbbbaabbbaaaaaabbaabbbaabbaaaabaab%bKGD- cmPPJCmp0712Hs IDATx^ێ8P1DH˨%Ԛ4o ]67)]*mҡM ;[)+Ek+" &e%XӤ@``L,iRVE @0MJIY 4)+" &e%XӤ@``L,iRVE @0MJIY 4)+" :WVWWtE&-A]@M.a Uޟu[Ĭ.1cku~ :鱿MGdA`YV=r=:]/4UVE-GڊXK6W1XK/uhb綺խ%BE2I:U7LV*{#-~X;͹.BZ0u])hjJUaa&8c7TU3,3uVD)/,xwb ZVU{KDCENU -VXuG@D8akAG~',#a)Z@Pv 5[,@VOhI*FX#5ƺaRE| U-.w*NX&|t Si,ӸT!S?{DXbv,>#.",šA\< Ta)Z1O%WXUHnE%YXJ\}a"joZ"\XJ!rV];xfir :zKw$&e!;5]KTk_3">,AR^6܌?ڰ!`` r^O aˎ͓;*8q*3~dU&,Ax*\҃9 \h7Gd5т%63V8kߕ ҂E _N;q@":d} isd35`c6w0뜃&yav4oa5Uk 0Th Vsy܁\8RS;i?FJYBwvqT'az,,[ͪZ1:1Nw6l Nxi)XH9#_NZsZ"ްؕ=a$*_ܚ9VV9BYO[+Xra3,HG#zrg D}@k;Nt)Snx?^e5}# -wR 8<F>@{`5PEvio,?p!EXc vM8aehA8au/ ` az7`as, -*N0 5*ITwjTi.5v:>,jް҄I Ӊlna%?9̨ڌ='\ AkHNE[\FH yq}FLRw@0PN x`AxOKV;b%^-XY厩Y`&gK/**:Xcw^09ပ<~uZff9\Q|8[BCMfnc g [ eGWZKy5Z[tXi^uۊX6QitX<,KU [ɰx:63e {aձ+=Ys)J[؇:6ZX&PdžwB#b';֋HrDXYբzDX=e)"rDX [q4X9 ovM(8liY6)V^`-W-( x!j$X!&gp8EF3^8xS`]QbN{\h`eμI ҇Xy3[ZX|bzD:|3NvwD:,EYAuݪ4-:,9*AdX"&W֐a1.P% ;{Ȱw2Z@`pol@*e^]t)Vlav\"}H(-"\+dk+ދk Ka (4X|+"ZE-H") +}@`ptlʤ> uC7zi{gX롂QgS` 3-A` -Z5~|ӣ ʂ|JD6Nq:Gw>s=(6x'V_f w!J1 $*0u:o5a,`7%?u47la]BÉ+p,8Vah)XO- Ij=d\XW Eyؚ _’3D7Lt~$O'.@: u$,|`U]8Xre&~tB-,*.1yWIX _[ "1>=RGn3o=V}X<\*Q&o[3coTDձp&?w8iHY@{A4kHN<5O.FXX6Ș \W,mZ [XMzuꊄ8p#,6M2n\+u9aפ_]ՃA^Qpj4}M2'mzj ,8K\lҽUu>#`ag{k /° ܩmLцB!Xw3=^™yܤk?. >] \>xknpҞ*^ŬMu=`/} , 1*(\w(8-\RC {ļ }}g\8ex'3|.Z7 @6u;ܟ֠2pǘXb/2ֵ}=GD] ) hd/k@il; eo֘Z)Še&),VX Aa7w}Hh ٦'VG87t}2kL4±anABlu>Om\raH&'μ6ƥ'eBwV@ˢlmsLGH_HX)ec%bI7-:p$Vߡ-++~R XrQeFÛ}.)MrMW+aM}Ϭ,6Ү9NZa!), 0Ue),*Ka! LUY AaRXSUB@?UKPJIENDB`tDd(X??V   C 2A ttest_output b3J`."Bn3J`."BPNG  IHDR(qnssRGBPLTEoTĻ;IDATx^іEmo'1HFl8}שׁJ@HG;1A)m_(SԾ/gԂ)jߗ3x|ʦjxفy΀Jm56K)`X? 6? xSԂT'~jyP_י8:f>=i&R{u-˜9;$}'U/ϬjBjjg Qۥ @`&F-2 4P+C}l>YwB@nj`]dwB/U̢Bnd= ]-EEʳ4zCu}W+I?\m`{nb+2"Y)ARԂ)jߗ3x j<`} Z0>@rA-x}9Ǡ OPcP ާ}_౺Kg3Ԗ벊V(ɍ={VwoHqujwG7%[hԞ3݋L"'e#0ZGn5`Ojv~@B:>er:23\s R{@mm/1 P hI,eҫ+\CJ+eo!+hEBJ7 1q{1gc);o{~n7|LqwxCq> #])SH> }rNv\ 'D j>}rNv\ 'D j>}rNv\ 'D j>}rNv\ 'D j>}rNv\ 'D{xq=sG=;FQsstǨ= wvG!1%@t4/z14)nH-@z~[FM-My/֑Z>S6ϰǻ涂=OC}K?CW o++֫Gk&`oa$ 4nZ1$Ԇo4\OqpD :f%ZǻܫUGȏѓcx M缚Md|ݱC511_/7#?k-daS$HJyv 9$0wG:Fd(GjD*#$TLL{e<5ռ@םLF:&{Sbi'|$7mXV?clۮ?%KiޏKq@CQcجjԨ,;v9ƅ -!WB^$asqXk[6l"ZYwk#k*ۨMүyR'5RAi6cv Fq$*o.FGEu4٧5:tɢέ@Dcԋ<-fFrk~cN*^?B/=D sO/W e[#S>]:^btC}(*Kȸ7?nN8ݎ^ F>Yx7 MCgAs]wGj@SԾ/gԂ)0!Fߧ-<O! 1>m(`t@:=,1%]KwDӣ}R={y(AZ#!1G>E:`':׍f]]ZS;nw <^TIS5pKqzP? l:硚R &z{#1h`wx}bBN=.r̸z0~Vx1 m B-k~Hv*&rģw$Z}=++HzZ3So?pY"Syϵ^.WWºDw-HT(f_WEFtH ^\ѧDpj.8 }I0Pٵpf NEs#Shv[RHš~kKT.tS"UT*vQ[\Пu_'*q_Yj%$QhcJ'lG58Ѻ&fGKa;M1obG1Q-ԲSZ}Y-.*&n8F kj1RNmQ:E "jJhơ_נ|uP&;g=X[D:d'{ګ8XԯQCXʦ hwdtxD it8\'2kIfmb__gEI8[RNb*̖qE(՗&V;hBϲc/ \^` 4+j%C ) favz @Y2t8Ь[Baͨ=@1jG=;FQsstǨ= wz=Nm8rT~ +T@ZqQ~깡I؛ pn0ڣ܊-

Muӊ j;rNהZܭWI~/8sAUX/߶Y'E5M<SJaXԖ'nimx'jü&&/di~v-R[Llct4ao$gUj8a_3VQ#&lJkmpitZVjkܣBmd6LhD؝iʯ&G֖ZT܇Z^QMt6F;bK AkdNog~ ܖʿqo=g¶UGmѶ-mQ m}FEE-}yſ5Khg;6=u0 vfvlt73Pۑ]`@mGnfwFGx=u0 vfvlt73Pۑ]`@mGnfwFGx=u0 N{tUrc\%1Gwƍqy 7ݒv,ݯUAl@cًY;g㾸b,ZZYn~ܹ7QU wDna ul]k$Q7hw{بQ+nU-UyWlKʺ*n5VoB]J6 j}DmqQJ~ڛ}Fgg/IxG-׋" )+Z$j3Q{C\:0Hʼ-u=WlV~ز{Wip Xr#71F{eػ%=Xn+?g^{,Xz²jۋz V`0엇5`6:D쮃og#7f#͠? [3fq۷9g f`ц+~hc<6l YSAKښ5=6l Y3w!mZo;vύg\Ec?N/_cc5sN]ƬFMS~Uvʍ±dB|A<=&0Zmh<,VY|A.zV7h gcŌnƸȶ{c5;qelzUvO*1[!/ ѡ`@mGnfwFGx=u0 V굧47S.vDu|C\!UK>l07Rkqڷg9 O.2 al,]*\^DhlF5쵹Q=hlTk 'g:͕KHjoV!tE^jsQOmsCW!ɥ"y" Zu}{\k=z<֢|ZK_4jՅo1Hj0NVj*pVa&4o B8jrL௓J"P[TpIu.y ^淋,gsqNµL?FjHk J:Z԰Nֵg˝Jy<:-BԨ﷘5<5_~(7֦%GQx1ƌ_E, aӻ˹U[ Ji^.>^Y^{Vi;chצt)%jb|wgm#7u 0 #7f#ڎ:{j;r3`6:쮃og#7f#ڎ:{j;r3`6:쮃og#7f#ڎ:{j;r3߿o4vìwOQj_GȂڷ!!vg =X} @V$ ԾZ g >Z >Z }0@PTjl93yV@EV%i kZTQ kB)j bTB)j bTB)j bTԞ|nIyʩw]RKbvO@2Z{)~Ъ$LOߘr>%MqX4!Woz1/oASp܅2ON/[;!Ə8 M9#-tmM㮯򚎡yY69ϰc3H),L yb0t)Y5>DӼ4 CސJe5ZZThCab*Z$J@5gZkOֵъı^ Kjh)尘&uF4ykTYl(@ҊΣtH}VZKU@Kʬ< ;=ѡ*[ >Ǣ 4r+[ɰeb#ݻ9Skl*R~.Yjg ȇsvmJȆ:Abd*elPk[kmkW%`6 &bDE@dHƐ{]xΆ+?LqaBHlԶR{O=A]q _뵢f )2U:rd1;IoG3'rQ]ovCD0Ȇť4WY3zR}LUc]+;Dw8ĈZW׈Ԯǽ{{hAmW|F9E3ce6Uނ Z,]oJi& 5Nĉ^HW {c7x (5v:rX̮ Ԫ<}侚>VR e\_I QVS)+7&V|u 1{,*p֞|IûzIzw>}uІbn$8~Buk Ԛ90LdF}$0K &1/hu/ @ Qs?'暩再xJK0a5dڨqM"Ejcw믢'Glٙ&7 ")^n_sH1Wof1iYK"hҝMGOΟcq吘<T2QY"!ʕj©9ɻCxyQ['Iw8߭lչ@!UQX־o0Ä>dlY4=ogRvvz @Y2t8Ьm +j4+j%C ) favz @Y2t8Ьm +j4+j%C ) favz @$@!{IENDB`DyK "ftp://username@unixs.cis.pitt.eduyK Fftp://username@unixs.cis.pitt.edu/DyK ftp://fmc2@unixs.cis.pitt.eduyK >ftp://fmc2@unixs.cis.pitt.edu/H@H 6 iNormal CJOJQJ_HaJmH sH tH Z@Z  Heading 1$<@&5CJ KH OJQJ\^JaJ \@\  Heading 2$<@& 56CJOJQJ\]^JaJV@V G; Heading 3$<@&5CJOJQJ\^JaJDA@D Default Paragraph FontRi@R  Table Normal4 l4a (k@(No List4 @4  Footer  !.)@.  Page Number6U@6 .V Hyperlink >*B*phe@" [_HTML Preformatted7 2( Px 4 #\'*.25@9CJOJQJ^JaJJOJ jTNormal1 *$1$7$B*OJQJphtHww 1:GXixCS LGHZj=K  t X8>sFGGnoEO7  67K!U!!!!Y"Z"""""# ##b$%''***,, -).////1144855555667778888893949_::;;;===AAAAzB{BBBRCTCCCCCC?DADD/EEIII-J.JJJKMMeQfQQQRR(SSTTTTTVVqWX XNXpXXXXXXYYYZZp[q[[[\^^^^p`q`bbfcgcvdwdeeeeeeDfEfghhNhOhnhohhhhhiijjjjjl7lln{n?oooqqqrtttuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuvvvvvvvvvvvvvvvvvvvv v!v"v.v/v0v1v2v3v4v5v6v7v8v9v:vFvGvHvIvVvWvXvYvZv[v\v]v^v_v`vavbvcvdvevfvgvhvivuvvvwvxvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvw w w w w wwwwwww w!w"w#w$w%w3w4w5w6w7w8w9w:w;wsGG  6U!!!" ##'***,\^^wdEfhhjjrttuvw0000000000 0 0@ 0@0@0z00@0@0@0@ 0@ 0z00@ @0@ 0@ 0@ 0@ 0@ 0@0@0R @0R @0R @0R @0R @0R @0R @ 0R @ 0R @ 0R ^~0A0^~0A0^~0>0^~0E0(^~0E0^~0>0^~0H0^~0H0^~0H0^~0H0(^~0H0^~0>0^~0L0^~0>0^~0>0:0/000 0 0 0 000000@0@0z0Y0@ z0Y0z0Y0@0@00zz  ]<$5),i49>FINT7WXd^dn pNrzM>0x@CEGIKLNOPRSUVXYZ\^_`boqsty~ o (.:BmJV^lyus4cKmADFHJMQTW[]aprxz{|}B 9 G /s`sssstwXXX !!8@0(  B S  ?w;|";L,#; /#;4#;;4B#;l";#;< <<$<7#<,"<<4#s s KOpppw     !0} QOpppw   8*urn:schemas-microsoft-com:office:smarttagsdate8*urn:schemas-microsoft-com:office:smarttagstime= *urn:schemas-microsoft-com:office:smarttags PlaceType= *urn:schemas-microsoft-com:office:smarttags PlaceName9 *urn:schemas-microsoft-com:office:smarttagsplace  0131920047DayHourMinuteMonthYear  or4 ? |X\(() )#*****=6I688g?i???@@>A@A(B*BBBCC[F]F'G)GGGIG.I0IIIJJ'L*LMMNNPPQQRR$Y&Y\\bb|ddnnoooooooEpqqqqqrr/sasssssttktltttuusuuuuuuuuuuuuu vv"v,v:vDvJvTvivsvxvvvvvvvvvvvvvvvwww&w1w=wHwTw_wowwwworCQ^zLm 9dko %"("""+(-(((((#*+***-M-z-}-55-72788==g?i???>A@AABBBCCDDEEEEE;F[F]F'G)GGG'H-HIIJJMMQRZTbT~WW`XbXXXY YYY,b0b)c.cXfZfWgYgiioooGpqqqrrttttsuuuuuuuuuuu vv"v-v:vEvJvUvivtvxvvvvvvvvvvvvvvvwww&w2w=wIwTw`wowwww3333333333333333333333333333333333333333333333333333333333PbbecgcddeefCfnwowwwzwwwwwwbbowwwwDana2W; hL'pZ+>VeEQގeKm7o&M R*uT?KRV}0WR0V^& bb;3k.N X6Pr6(ZsdG)wtun6h^`OJQJo(hHh^`OJQJ^Jo(hHohpp^p`OJQJo(hHh@ @ ^@ `OJQJo(hHh^`OJQJ^Jo(hHoh^`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohPP^P`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohpp^p`OJQJo(hHh@ @ ^@ `OJQJo(hHh^`OJQJ^Jo(hHoh^`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohPP^P`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohpp^p`OJQJo(hHh@ @ ^@ `OJQJo(hHh^`OJQJ^Jo(hHoh^`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohPP^P`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohpp^p`OJQJo(hHh@ @ ^@ `OJQJo(hHh^`OJQJ^Jo(hHoh^`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohPP^P`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohpp^p`OJQJo(hHh@ @ ^@ `OJQJo(hHh^`OJQJ^Jo(hHoh^`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohPP^P`OJQJo(hHh^`OJQJo(hHh ^`o(hH)hpp^p`OJQJo(hHh@ @ ^@ `OJQJo(hHh^`OJQJ^Jo(hHoh^`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohPP^P`OJQJo(hH^`.^`.pp^p`.@ @ ^@ `.^`.^`.^`.^`.PP^P`.^`.^`.pp^p`.@ @ ^@ `.^`.^`.^`.^`.PP^P`.h^`OJQJo(hHh^`OJQJ^Jo(hHohpp^p`OJQJo(hHh@ @ ^@ `OJQJo(hHh^`OJQJ^Jo(hHoh^`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohPP^P`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohpp^p`OJQJo(hHh@ @ ^@ `OJQJo(hHh^`OJQJ^Jo(hHoh^`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohPP^P`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohpp^p`OJQJo(hHh@ @ ^@ `OJQJo(hHh^`OJQJ^Jo(hHoh^`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohPP^P`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohpp^p`OJQJo(hHh@ @ ^@ `OJQJo(hHh^`OJQJ^Jo(hHoh^`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohPP^P`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohpp^p`OJQJo(hHh@ @ ^@ `OJQJo(hHh^`OJQJ^Jo(hHoh^`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohPP^P`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohpp^p`OJQJo(hHh@ @ ^@ `OJQJo(hHh^`OJQJ^Jo(hHoh^`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohPP^P`OJQJo(hH^`.^`.pp^p`.@ @ ^@ `.^`.^`.^`.^`.PP^P`.h^`OJQJo(hHh^`OJQJ^Jo(hHohpp^p`OJQJo(hHh@ @ ^@ `OJQJo(hHh^`OJQJ^Jo(hHoh^`OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHohPP^P`OJQJo(hHh ^`hH.h^`OJQJo(hHh pLp^p`LhH.h @ @ ^@ `hH.h ^`hH.h L^`LhH.h ^`hH.h ^`hH.h PLP^P`LhH.6eKeEX6Pr7o&M)w0WR+>?KR;3kV^ RZs2WbL';                                                                                                                               7R/jIZ8?GoGNeGH G77Q;FC $z fL S T\  P l7a<@ qT.* Ktx+AdAQH_`k?g^f jvyh nJ[ a| )!)+!_Z!P"_q"N^$&nI&G-'(&)8)o*C+#+/+/U+,0,e9,S,0112@23_3B@4F4Pe41595zG67V}768;8H8F49r97O:lf:n;U<= =:@=%6?@8AxABr"BGBQBwB>CQC?JDrG H IJRKL$L(MBNZ{NO%O P0XQkQ[S(TjTdUVVEVLW8X"YZYoY:sY5vY=ZQZW [ [[\3#\]b]]^(^bW^_\^n^EE`PaWab(b$b>b[bymbob ~cd Vdhdde<f-g?g6 i?iTktkD2o!qBq}qCr{"satdtwgt8&uRu|^u %xq>d^4j+6R]~9J7$Izc*y e>$KwJv AKyeHw(MK U/bob0F5iW^@z40 -WH"c;.]U!\fe.o|ADZsp0tBjCXqc3hT`PJ'A)RqV6"KLZOpCPZ2r,IM_Mf} a.V_x=/@bbH?)bbVV^+^,/045678)B)C)G)H)INOPQWXY]^/b/c/e/f/h/iuw@@@&@P@@6@p@@<@|@@B@D@F@H@@@T@@@Z@\@@@d@@@h@@@p@r@@@x@@@~@@@@@@@@@UnknownG: Times New Roman5Symbol3& : Arial?5 z Courier New5"System;Wingdings"qhx|FDy5e=e=Y24d2w2w 3QH)?\ZCLRES 2020 Lab 1 : DanaDanaP            Oh+'0t  0 < HT\dlCLRES 2020 Lab 1 : LREDana 20anaanaNormal0Danal0377Microsoft Word 10.0@~7@XX#S@jVke՜.+,D՜.+,X hp  University of Pittsburghe=2w CLRES 2020 Lab 1 : Title 8@ _PID_HLINKSAT ftp://fmc2@unixs.cis.pitt.edu/z#ftp://username@unixs.cis.pitt.edu/[*mailto:fmc2@pitt.edu  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%'()*+,-/012345:Root Entry FVk<Data 1Table-WordDocument" SummaryInformation(&DocumentSummaryInformation8.CompObjj  FMicrosoft Word Document MSWordDocWord.Document.89q