The question
Name: ______________________ Date: ____________ Exercise and sleep quality: a chi-square test for independence (10 points)
Table
Exercise and sleep quality
A health agency selects a random sample of 500 adults in a large state. Each adult reports how many days a week they exercise for at least 30 minutes and rates their usual sleep quality. The agency wants to know whether exercise and sleep quality are associated for adults in the state. (Invented data.)
| Exercise | Poor sleep | Fair sleep | Good sleep | Total |
|---|---|---|---|---|
| None | 52 | 58 | 40 | 150 |
| 1 to 2 days | 45 | 70 | 65 | 180 |
| 3 or more days | 30 | 62 | 78 | 170 |
| Total | 127 | 190 | 183 | 500 |
(a) State the null and alternative hypotheses for a test of whether exercise and sleep quality are associated. [1 point]
(b) Identify the appropriate test and calculate the expected count of adults who do not exercise and report poor sleep, showing your work. [2 points]
(c) Verify the conditions for the test. [2 points]
(d) Calculate the chi-square statistic, the degrees of freedom and the p-value. [2 points]
(e) State the conclusion of the test at the significance level 0.05, in context. [2 points]
(f) Describe the association, using the cells that contribute most to the chi-square statistic. [1 point]