Part I

Use the dataset in the “Class Survey” Excel file, which contains an in-class survey of introductory statistics students. Detailed variable definitions and question wording are included in the file.

1) How many males and females are there?

2) Create a crosstab of counts of “like cats” by “male or female”. Please properly format your table (i.e. no “0” or “1”. Use proper labels for “male”, “female”, “likes cats”, “does not like cats”).

3) What proportion of all students in the dataset like cats? What proportion of male students like cats? What proportion of female students like cats?

4) Create a 99% confidence interval for the proportion of statistics students who like cats, and interpret the interval.

5) Do an appropriate analysis at the 0.10 level of significance to see whether “liking cats” is a

different proportion for males vs. females.

6) Create a 90% confidence interval for the difference in proportion between males and females that like cats. Interpret it.

7) Compare your answers to (5) and (6) and explain the connection between the two. (Hint: you need to be mentioning whether 0 is in the interval).

8) Check the validity of the data in the GPA field and explain how you treat special cases.

9) What’s the average GPA for all students in the dataset? What’s the average GPA for males? What’s the average GPA for females?

10) Create a 95% confidence interval for the GPA of statistics students and interpret the interval.

11) Perform an appropriate analysis (an F test) to see if there is a difference in variability in GPA for males vs. females at the 0.10 level of significance.

12) Perform an appropriate analysis with an appropriate t test to see if there is a difference in GPA for males vs. females, at the 0.10 level of significance. (Hint: Use the results of the F test to know which t test to use).

Part II

This is an experiment to illustrate the Central Limit Theorem.

1) State the Central Limit Theorem and explain what it means in your own words.

2) Use =RANDBETWEEN(1, 100) to create 250 samples of size ???? = ???????? each by choosing generating random integer (whole) numbers between 1 and 100.

3) What theoretical distribution are you using when you do this? What are the

mean and SD of this theoretical distribution?

4) Make a histogram of 7500 integer values you generated. Use bins 10 units wide. Describe the shape of this distribution and calculate the sample mean and SD from the data you generated. Are these values similar to the theoretical values you found in (3)?

5) For each sample, calculate the mean. (There should be 250 sample means.)

6) Make a histogram of your 250 sample means using bins 5 units wide.

7) Discuss the histogram shape. Create a normal probability plot for the sample means. Does the Central Limit Theorem seem to be working?

8) Find the mean of your 250 sample means. What value should it be, according to the central limit theorem? Was it what you would expect?

9) Find the standard deviation of your 250 sample means. What value should it be, according to the central limit theorem? Was it what you would expect?

Please remember to label all your answers and graphs accordingly! Use the proper symbols, formulas and terminology.

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