StatCrunch Assignment 3 | Complete Solution

StatCrunch Assignment 3

In this assignment, you will use the StatCrunch U data set that you developed in Module 2 as part of the first StatCrunch assignment.

As you did in StatCrunch Assignment 1B, look at the items in the StatCrunch U survey and develop a question regarding population proportions that can be answered using the survey data you collected.

As a reminder, here are the items on the survey:

Here are some possible questions.  Feel free to pick one of those questions—but it would be better for you to formulate a question of your own. For this assignment, you need a question related to proportions and one that will require the use of a confidence interval and hypothesis test to answer. NOTE: There is a sample StatCrunch Assignment 3 designed to give you an idea of how to do this assignment. It uses a question related to the proportions of female and male students at StatCrunch U. You cannot use that question on this assignment.

·         Is the proportion of seniors less than the proportion of freshman?

·         Is the proportion of male students who work different from the proportion of female students who work?

·         Is the proportion of students with student loans who work greater than the proportion of students without student loans who work?

·         Is the proportion of female students with credit card debt greater than the proportion of male students with credit card debt?

·         Is the proportion of male freshman students different from the proportion of male senior students?

Answer each of the following questions. Point values are indicated with each question.

1.    (20 pts.) State your question. Remember that your question should be related to the population proportion or proportions and should be one that will require the use of a confidence interval and hypothesis test to answer. Assume that your sample is representative of the population.

2.    (30 pts.) Explain the methodology you will use to answer the question you posed. Your explanation should include answers to the following questions. Do not include your analysis or answers to your question here—only describe how you will do the analysis.

·         What is the variable of interest?

• What confidence interval will you use?
• What are your null and alternate hypotheses?
• Is it a one-sample or two-sample test?
• Is it an upper (right)-, lower (left)-, or two-tail test?
• What level of significance will you use and why?
• Are the conditions necessary for a confidence interval and hypothesis test for the population proportion satisfied? Explain.

3.    (30 pts.) Carry out the methodology described in 2 above. Use StatCrunch and paste copies of the StatCrunch output in the space below. (NOTE: For the purposes of this assignment, go ahead and complete the confidence interval and hypothesis test even if there are not at least 10 successes and 10 failures.) Your explanation should include answers to the following questions:

·         What are the upper and lower bounds of the confidence interval?

• What is the error term in the confidence interval?
• What does the confidence interval mean in terms of the question you posed?
• What is the p-value in your hypothesis test and what does it mean in terms of the question you posed?
• Did you reject or not reject the null hypothesis and why?
• What is the conclusion of your hypothesis test in terms of the question you posed?
• Do the results of the confidence interval and hypothesis test agree? Explain.

4.    4. (20 pts.) Based on the results of 2 and 3 above, answer your question. Include an explanation of how you used the StatCrunch output to formulate your answer.

DATA:

ID Gender Class Hours Work Loans CC Debt
1932 Female 4 14 0 14931 1981
2358 Male 4 20 0 0 8809
5286 Female 4 4 40 15517 4196
5422 Female 4 14 0 0 8651
6015 Male 1 16 0 0 1774
7500 Male 1 18 11.5 0 0 1253
13773 Male 3 9 26 0 5019
14857 Female 1 14 0 4362 1205
15683 Male 4 12 20 0 5461
17339 Male 3 18 0 13328 3217
17771 Female 1 10 16.5 2778 1025
18326 Male 3 11 20 12228 3878
19670 Male 4 5 29.5 15461 9777
21236 Female 3 15 0 11370 4959
21960 Male 3 11 22.5 12926 0
22509 Male 2 12 0 7964 2895
22926 Female 1 18 0 0 1214
24400 Male 2 21 0 0 2600
24906 Male 1 18 10.5 3044 1516
26589 Male 3 12 15 0 2630
29877 Female 1 17 0 0 1084
30310 Female 3 17 0 0 0
30450 Female 4 12 0 0 6339
30830 Female 4 18 0 0 3240
32693 Female 3 14 16 11310 5143
36751 Female 4 12 0 0 9606
42624 Female 1 20 7 0 1375
44325 Female 3 14 16.5 0 4983
45182 Female 3 15 17 10943 3760
45568 Female 4 14 0 0 4449