Math 224 – Elementary Statistics



Statistics – Lab #7

Statistical Concepts

← Confidence Intervals

← Hypothesis Testing

Calculating Confidence Intervals for one Variable

➢ Open the class survey results that were entered into the MINITAB worksheet.

➢ We are interested in calculating a 95% confidence interval for the hours of sleep a student gets. Pull up Stat > Basic Statistics > 1-Sample t and set Samples in columns: to Sleep. Click the OK button and the results will appear in your Session Window.

➢ We are also interested in the same analysis with a 99% confidence interval. Use the same steps except select the Options button and change the Confidence level: to 99.

Performing Hypothesis testing for one Variable

➢ We want to test and see if the average sleep a student gets in a night is less than 8 hours. Pull up Stat > Basic Statistics > 1-Sample t and set Samples in columns: to hours of sleep. Check Perform hypothesis test and in the text area, enter the value 8. Click on the Options button and less than for the Alternative:. Click each OK button and the results will appear in your Session Window.

Calculating Confidence Intervals and Performing Hypothesis testing for two Variables

➢ Calculate descriptive statistics for the variable hours of sleep by gender. The output will be displayed in the Session Window. This output is useful to see if it can be assumed that the two groups have equal variances.

➢ We are interested in calculating a 95% confidence interval for the difference in hours of sleep between male and female students. We also want to test and see if this difference does not equal zero. Pull up Stat > Basic Statistics > 2-Sample t and set Samples: to the hours of sleep variable and set Subscripts: equal to Gender. If you think we should assume equal variance then check the Assume equal variances check box. This output will also be displayed in the Session Window. Print out a copy of the Session window that includes all of the analysis done in this lab.

Short Answer Writing Assignment

If applicable, answers should be complete sentences. Include a copy of the print out with this assignment.

1. Give and interpret the 95% confidence interval for the hours of sleep a student gets.

2. Give and interpret the 99% confidence interval for the hours of sleep a student gets.

3. Compare the 95% and 99% confidence intervals for the hours of sleep a student gets. Explain the difference between these intervals and why this difference occurs.

4. Give and interpret the p-value at [pic] for the hypothesis test where we wanted to see if the average hours of sleep is less than 8.

5. If you use [pic], does your interpretation in question 4 change? Explain your reasoning.

6. Give the variance for hours of sleep for each gender. Do you think that we can assume the population variances are equal? Explain your reasoning.

7. Give and interpret the 95% confidence interval for the difference in hours of sleep for males and females.

8. Give and interpret the p-value at [pic] for the difference in hours of sleep for males and females.

9. If you use [pic], does your interpretation in question 8 change? Explain your reasoning.

10. Explain the relationship between confidence intervals and hypothesis tests using the answers to questions 7 and 8. Be sure to explain how you can tell the outcome of the hypothesis test by looking at the confidence interval.

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