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6* # d 6 9 X: 0 : 6 B? L B? @ 8 8 & B? 8 h : : h : B? | : Stats 95 Assignment 1
Imagine you have collected data from a UX study and summarized it in the table below.
Part # PositionGender Age Group ExperienceSubjective Rating of PerformanceErrors CommittedTime (sec)1EmployeeFemale 20-30expert8104578.342EmployeeMale 31-40novice676345.543Manager Female 31-40interm8110564.334Senior Manager Male 31-40interm363523.775EmployeeMale 41-50novice5671034.096EmployeeFemale 41-50interm568323.347Manager Female 41-50expert693224.448Senior Manager Female 51 and aboveinterm8108939.439EmployeeFemale 51 and aboveexpert795467.45
Label the data type for each column (excluding the Participant column).
Create a 2 (Gender) x 3 (Position) bar graph and a 2 (Gender) x 3 (Expertise) bar graph, either by hand or by using the pivot table in the Excel document Assignment 1 Usability Table on the class website.
Create a scatter-plot using the Time as the predictor (X-axis) and Errors Committed as the criterion (Y-axis), either by hand or by using the pivot table in the Excel document Assignment 1 Usability Table on the class website.
Section 1Section 262687376698297636199909185938085778271787377526466775558767384897681697270786570Scenario: Dr. Torres teaches two sections of Stat 95 at SJSU. After grading the first exam, he wants to compare the two sections to see which one performed better on the exam. Use the data below to help Dr. Torres compare the two sections. The data represent percentages on the exam.
Summary of Tasks:
Compute the mean, median, mode, minimum, maximum, range, and standard deviation for each group.
Create a histogram for each distribution.
Answer the following questions using the data and graphs.
Questions (Be sure to use complete sentences):
Describe the center of each distribution, be sure to mention:
What are the mean, median, and mode for each distribution?
Look at the frequency distribution table. What is the most frequently occurring score in each distribution? What percent of students in each section received this score?
Name the measure of central tendency that divides the top 50% from the bottom 50% of scores.
Based on these measures of central tendency, which Section performed better? Explain your answer.
Describe the variability in each distribution, be sure to mention:
What is the minimum and maximum score in each distribution?
What is the range for each distribution? What does this measure tell us about the dispersion of scores in each distribution?
What is the standard deviation for each distribution? What does this measure tell us about the dispersion of scores in each distribution?
Which Section displays more variability? Explain your answer.
Describe the shape of each distribution, be sure to mention:
Based on the three measures of central tendency, are the distributions approximately normal or are they skewed? Explain your answer.
Based on the histograms, do the distributions appear approximately normal or skewed? Explain your answer. Does this answer agree with your answer to the previous question?
Generate a box-plot, and identify the scores at each quartile for section 1 and Section 2.
Please generate by hand a stem-and-leaf plot for Section 1.
Z-scores and Probability
Using a normal distribution, and the Z-table at the back of the book, answer the following questions.
What percentile is associated with a z-score of:
+2
-2
+1
What is the percentage of the population between the Mean and the z-score of:
+1.68
-2.45
What percentage of the population in a normal distribution is between two z-scores of:
+2 and +3
-2 and +1
-1.78 and +1.69
+1.15 and 1.85
What probability of randomly selecting an observation from a population with a Z-score:
e" + . 2 , + . 8 7 , 1 . 6 5 , 1 . 9 6
d" - 2 , - . 9 2 , - 1 . 6 5 , - 1 . 9 6
C e n t r a l L i m i t T h e o r e m E x e r c i s e .
L e a r n i n g O b j e c t i v e s : ( 1 ) T o l e a r n h o w t o e n t e r d a t a i n t o E x c e l ; ( 2 ) T o l e a r n h o w t o g e n e r a t e a r e c t a n g u l a r d i s t r i b u t i o n o f r a n d o m n u m b e r s f r o m 0 - 1 0 . ( 3 ) T o s i m u l a t e a d istribution of sample means from a distribution (4) to compare the shape, central tendencies and variability of both distributions to the outcomes expected by Central Limit Theorem.
Using an Excel sheet, generate three distributions of 90 random variables 0-10. For each of the distributions, create a distribution of sample means, N = 3. For each of the three distributions of individual scores and distributions of sample means:
Use SPSS to provide: minimum, maximum, range, mean, mode, median, variance, standard deviation, and the histogram of both distributions. Do not print out all the raw data, just a table with the required statistics and the histogram. To save paper, try to get all the graphs on the same page, you can usually do this by shrinking the graph or using the Snipping Tool.
Describe the shapes of the frequency distribution of variables and the frequency distribution of sample means. What is the difference between the two shapes, and how does the Central Limit Theorem explain that difference? Compare the means of both distributions, do they match the predictions of Central Limit Theorem? Compare the standard deviation of both distributions. Use the standard deviation of the first distribution to calculate the value of the standard deviation of the sample means predicted by Central Limit Theorem, and compare this predicted value to the actual value.
Randomly select two variables from each distribution, one ABOVE and one BELOW the mean of each distribution, calculate the appropriate Z-score (individual variable) and Z-statistic (sample mean). Use the Appendix at the back of the book to identify the probability for each.
Show the calculations for the z-scores and z-statistics.
Lady Tasting Tea Chapter 1
What problems did Fisher have to tackle in the designing the experiment that could determine if the Lady could distinguish between milk-then-tea and tea-then-milk cups of tea?
In examining the fertility index and rainfall records at Rothamsted, what two main errors did he conclude about the indexes and how did he express results about the rainfall?
What did Fisher conclude scientists needed to start with to do an experiment, and what would a useful experiment do?
Critical Reasoning
An elementary school teacher is interested in the relation between sugar consumption and activity level in preschool children. The teacher gives 30 preschool children from the Preppy Preschool Playland either 0 milligrams, 20 milligrams, or 50 milligrams of sucrose (i.e., sugar) in a breakfast drink. He then observes their behavior for 30 minutes during their morning outdoor play period and codes their activity level. Identify each of the following for this study:
a. The population
b. The sample
c. The independent variable
d. The levels of the independent variable
e. The dependent variable
Schacter and Gross (1968) gathered data from a group of 60 male students for about one hour in the afternoon. At the end of this period of time, a clock on the wall was correct (5:30 PM) for 20 participants, slow (5:00 PM) for 20 others, and fast (6:00 PM) for 20 more. The actual time for all groups was 5:30, the usual dinnertime for these students. While participants filled out a final questionnaire, the experimenters provided Wheat Thins for the students to eat. The weight of the crackers each student consumed was measured. The means were: 5:00 group 20grams; 5:30 group 30 grams; 6:00 group 40 grams. Identify each of the following for this study:
a. The population
b. The sample
c. The independent variable
d. The levels of the independent variable
e. The dependent variable
f. The descriptive statistic
g. Any inferences warranted by this study
Identify at least one confounding variable that undermines the conclusion drawn in the following fictional study description: Prof. Martin was interested in which of two popular statistics textbooks (Statistics: It Will Change Your Life and Statistics: Bigger, Better, Stronger) was better for students. Prof. Martin compared the two texts by assigning one text to a section of statistics taught by Prof. Miller at 10:00 AM on MWF and the other text to a section of statistics taught by Prof. Mervin from 7-10 PM on Wednesday evenings. At the end of the term, all students took the same comprehensive test. Students who were assigned Statistics: Bigger, Better, Stronger performed better on the test than did students who were assigned Statistics: It Will Change Your Life. Prof. Martin therefore concluded that the former textbook was the better one.
The following figure appeared on the Statistics Canada Web site. Evaluate the figure. What aspects of the figure should be changed so it more clearly depicts the data?
Figure: Absenteeism Rates Up
What is meant by a representative sample? Why is it important to obtain a representative sample?
What is the difference between a Type I and a Type II error? Which kind of error is more likely to be published and why? Give an example of each, and describe a situation that makes these kinds of errors dangerous.
Tips on Using Excel
To Generate Random Numbers
Pick a cell and type in the cell the following formula: =RAND()*10. Be sure to include the equal sign. This formula will generate random numbers between 0-10.
To Copy and Paste Cell
Move the cursor over the cell. You will notice the arrow changes to a Swiss cross, then if you place the cross over the bottom right corner of the cell, the Swiss cross becomes a cross-hair (looks like a plus sign). When your cursor is in cross-hair mode, Left Click and drag the cell. This will replicate the contents of the cell, including formulas like random generators, in this case a random generator between 0-10. Scroll down, until you have generated 90 random numbers between 0-10.
How To Generate Sample Means With Sample Size Of 3
Return cursor to top of column of random generated numbers, Select cell one column over (ie., select an empty cell right next to the column you generated).
Select Auto Sum(Average. A selection box will appear of the numbers Excel is guessing you want to average. Drag the selection box to include 3 random generated numbers. This generates a sample mean, sample size = 3.
Replicate the sample means for all 90 scores. You will Select three cells (two empty cells followed by a the sample mean). Place the cursor over lower right corner of selected cells, and the cursor will turn into the cross-hair mode. Drag to the end of adjacent column You should have 30 individual averages, each preceded by two empty cells.
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