StatCrunch U is a fictitious university made up of 46,000 students (the population). Each student completed the survey shown here:
Student survey
1. What is your gender?
m Female
m Male
2. What is your classification?
m 1 - Freshman
m 2 - Sophomore
m 3 -Junior
m 4 - Senior
3. How many credit hours are you taking this semester?
4. How many hours do you work each week? Please provide your answer to the nearest half hour.
5. What is the total amount (in dollars) of your student loans to date?
6. What is the total amount (in dollars) of credit card debt you have accrued to date?
Next go to your StatCrunch My Data folder and find the file so that you can work with it to answer the following questions.
1. Copy and paste the first 15 rows from your StatCrunch data file below. You can do that by highlighting the data in StatCrunch, then clicking on Edit>Copy. Next return to this file, place your cursor in the space below, and click Paste. The purpose of this is to allow your instructor to see the first part of your data set.Use all 200 students in your sample to answer the remaining questions.
2. What is the shape of the distribution of credit hours? Compute summary statistics and use StatCrunch to construct a histogram of the credit hour data. Include a short paragraph answering the question.
3. Suppose you want to construct a 95% confidence interval for the mean credit hours taken by StatCrunch U students. What sample size would be needed to limit the margin of error to 0.5 credit hours? Use the sample standard deviation from your sample as an estimate of the population standard deviation. You will need to follow the example on page 266 of the text.
4. (a) What is the proportion of females at StatCrunch U? Create a pie chart showing the proportion of female students at StatCrunch U. Be sure to include a couple of sentences answering the question.
(b) Does the proportion of females change across classes? Create a stacked bar chart and a contingency table to show how the proportion changes across classes. Make sure your bar chart shows proportions or percentages, not counts. Be sure to include a couple of sentences answering the question.
5. Does the number of credit hours taken vary depending on whether or not students work? Create two boxplots on the same set of axes showing the number of credit hours taken by students who work and by students who do not work. Describe the distributions and any similarities or differences.
6. Does the mean number of credit hours taken by all students appear to be significantly below 15? Use StatCrunch to conduct a one-sample t-test. Be sure to state the null and alternate hypotheses, include the output from StatCrunch, and briefly answer the question including justification for your answer.
7. For students who work, are there differences in the average loan amounts across classes? Use StatCrunch to conduct an ANOVA test to answer this question. Be sure to state the null and alternate hypotheses, include the output from StatCrunch, and briefly answer the question.
8. For students that work, is there a relationship between the dollar amount of loans they have and the number of hours per week that they work?
To set up this problem, you will need to use the Bin(Work) column you created in Problem 5. Open the StatCrunch U file and go to Stat>Regression>Simple Linear as shown to the right. In the menu that appears, select the x-variable, the y-variable, and complete the "Where" entry as shown. Include the StatCrunch output in your paper and be sure to briefly answer the question and explain your answer.
• Construct a scatter plot with Work Hours on the x-axis and Loan Amount on the y-axis.
• Compute the coefficient of correlation, the coefficient of determination, and the linear regression equation.
• Does there appear to be a relationship between work hours and loan amount? Explain your answer.
• Explain the meaning of the coefficient of determination as it applies specifically to this problem.
• Explain the meaning of the slope in the regression equation as it applies specifically to this problem. Is this the relationship you expected? Explain. If it isn't what you expected, explain why it might have occurred.
• Does a linear model appear to be appropriate for this comparison? Explain.
9. For students with credit card debt, does there appear to be a difference in the mean amount of credit card debt based on gender of the student? Conduct an appropriate two-sample t-test. Be sure to state the null and alternate hypotheses, include the output from StatCrunch, and briefly answer the question.
10. Is there evidence of a relationship between class and whether or not students work? Conduct a chi-square test of independence. State the null and alternate hypotheses, include StatCrunch output, and explain the results of your test.