ࡱ> 352c %bjbj "Rjj!fl@@@T((((,T<T?D:? a. plot the data on the graph, the data points for the years, 92, 93, and 94 dont seem to fit the pattern. b. most of the ratios are a bit over 1, 1.06 is the average for the 1st 8 data points b. (2nd b) table of values of years vs logy c. EMBED Equation.DSMT4 , r = .986, r2=.9726 (to plot the line use (1984, 3,04) and (1991, 3.217) d.  EMBED Equation.DSMT4  e.1410.847 (thousands) = 1,410,847 f. 78 a.  EMBED Equation.DSMT4 , r = -.9996, r2 = .9992,  EMBED Equation.DSMT4  b. the intensity of the light bulb decreases as the distance from the light bulb increases, a. 11,374,000 b. 51.2% c. 60,7%, 22.1%, 68.4%, 11.0% the 18-21 year old group comprises 60.7% and 68.4% of the 2 yr full or 4 yr full time students which is what we would expect, they are the majority of the students, they make up only 22.1% and 11.05 of the part-time students, part-time students are usually adults who have a family or are also working so dont have time to be a full-time student definitions- get from book a. population is the people who live in Ontario, sample are the 61,239 people who filled out the survey b. since the sample is so large, we can be fairly sure that the results of the survey would be a good reflections about the population c. This is an observational study because no treatment was imposed upon the subjects Control, Randomization, Replication a. Use the digits 0-9, let 0 and 1 represent that she passes, and 2-9 represent that she fails b. simulation results in a proportion of approximately .4 or 40% likelihood of passing c. 1st attempt (passing 0, 1), 2nd attempt (passing 0, 1, 2), 3rd attempt (passing 0, 1, 2, 3) approximately .66 or 66% a. Experimental subjects physicians, factor aspirin (pill given) two levels, response heart attack? b. diagram or explain how to design diagram or explain how to design a. o b. 1 c.0.01 d. 0.99 any example a. P(A or B) = P(A) + P(B) P(A and B) b. P(A and B) = P(A) * P(B) or P(A and B) = P(A) * P(B|A) c.  EMBED Equation.DSMT4  a. .445 b. .555 c. .314, .686 not independent because P(A)*P(B) = .38073, a. .5264 b. .4054 c. not independent 18. a. b. .8, .2, .4, .2, .2, .4  19. discrete are the counting numbers (whole numbers), continuous are all the real numbers (can include fractions) 20. a. .25 .39 .74 .61 .9, .65 mean = 4.66, SD = 1.202, Var = 1.444 21. a. mean = .001, SD = .0022369 mean = 2.0005, SD = .0011189 22. a. n = 10, p = .25 create a chart with 3 columns (x, P(x) using binompdf, CumP(x) using binomcdf) and the 2 histograms, one for the pdf and one of the cdf .2816 .5256 mean = 2.5, SD = 1.369 23. a. must have 2 categories, success and failure, P(success) must the same for each trial, all trials are independent, continue trials until the first success occurs, (no limit to n) create a chart with x, P(x) using geometpfd, cumP(x) using geometcdf and the two histograms for n up to 10 .08192 .6723 mean = 5 24. N(0, 1) for standard normal, area under the curve = 1, draw a curve 25. a. .12100 b. .1587 .6944 1.00 appox 0 .000005131 26. a. 80 .71374 .00774 12.5127 27. as you increase your sample size, the sample statistic will get closer to the true population parameter, when applies to sampling distributions it means that the mean of the sampling distribution can be used to estimate the population mean 28. CLT is a theorem that says if you take many simple random samples of size n from a population, the mean of the samples can be used to estimate the population mean, the sampling distribution will be normally distributed with a mean = to mu and a SD decreased by the sample size, the sampling distribution will be normal no matter what kind of distribution the population has 29. a. an unbiased statistics is one that is obtained from a SRS, so we want a statistic that is unbiased because we want to make a prediction about the population not always, the sample size will have an influences in the final estimating of the population parameter mean = 11.967, SD = 1.886,  EMBED Equation.DSMT4 =.4167 30. answers are the formulas for the standard deviation of the sampling distribution 31. sample statistic ME  EMBED Equation.DSMT4  population parameter  EMBED Equation.DSMT4 sample statistics + ME 32. a. 7.78  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4 8.62 if you were to take 100 samples form the same population and every sample was of size 50, then 95 of the sample would have a mean between 7.78 and 8.62 narrower because the critical value would be 1.645 instead of 1.96 so the ME would be smaller z= .9428, p-value = .3458, so Fail to Reject 33. a. .73  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4 .81 z = -2.12, p-value = .03400, so Reject 34. use the z-test when the sample size is large and/or the population SD is known, use the t-test when the sample size is small and the population SD is not known 35. ME is the amount of variation above and below the sample statistic where the actual population parameter should be when the samples of size n are taken 36. a. .6437  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  1.3563 t = 7.2424, p-value = 4.566*10^-12, Reject 37. a. t = 2.929, p-value = .00297, so Reject t = .1501, p-value = .44077, so Fail to Reject t = .6177, CI = .23  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4  1.47 Type I means you reject the null and you shouldnt have because it is the acceptable hypothesis, consequences would be that we would say there is a difference in 0 and 2 hours when there really isnt, so may choose to cool the chicken before cooking when you shouldnt Type II means you fail to reject the null and you should have, we believe that cooling for 8 hours to 24 hours is the same when it isnt, so you would most likely cool only 8 hours to save money when you should have cooled longer 38. a. t = 211.24, p-value is appox 0, so Reject 106.83  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4 108.57, since 50 is not within the CI, Reject the null 39. z= 6.826, p-value = 4.389*10^-12, Reject 40.  EMBED Equation.DSMT4 =11.24, p-value = .0105, Fail to Reject (barely) 41.  EMBED Equation.DSMT4 =6,8519, p = .23188, Fail to Reject 42. a. slope = -0.34655, y-int = 4.8615 b.  EMBED Equation.DSMT4 =4.8615 0.34655 x slope models  EMBED Equation.DSMT4 , y int models  EMBED Equation.DSMT4  -.47  EMBED Equation.DSMT4   EMBED Equation.DSMT4   EMBED Equation.DSMT4 -.22 t = -5.9077, reject .4 .2 .2 A B .2 .2 ;= ! " 9 : ; < I J ! 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