Depression. A study published in the Archives of General Psychiatry in March 2001 examined the impact of depression on a patient's ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4 years. Of the 361 patients with no depression, 67 died. Of the 89 patients with minor or major depression, 26 died. Among people who suffer from cardiac disease, are depressed patients more likely to die than nondepressed ones?

(d) Test the hypothesis and state your conclusion.

Depression revisited. Consider again the study of the association between depression and cardiac disease survivability in Exercise 20.

1. Create a \(95 \%\) confidence interval for the difference in survival rates.
2. Interpret your interval in this context.

#26: Retirement. The Employee Benefit Research Institute reports that \(27 \%\) of males anticipate having enough money to live comfortably in retirement, but only \(18 \%\) of females express that confidence. If these results were based on samples of 200 people of each sex, would you consider this strong evidence that men and women have different outlooks?

1. Test an appropriate hypothesis and state your conclusion.
2. If you concluded there was a difference, estimate that difference with a confidence interval and interpret your interval in context.
   #34: Doritos. Some students checked 6 bags of Doritos marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.2, 28.5, 28.7, 28.9, 29.1, 29.5.
   b) Find the mean and standard deviation of the observed weights.
3. Create a \(95 \%\) confidence interval for the mean weight of such bags of chips.

#40: Yogurt. Consumer Reports tested 14 brands of vanilla yogurt and found the following numbers of calories per serving:

b) Create a \(95 \%\) confidence interval for the average calorie content of vanilla yogurt.

c) A diet guide claims that you will get 120 calories from a serving of vanilla yogurt. What does this evidence indicate? Use your confidence interval to test an appropriate hypothesis and state your conclusion.

Page 614, #41: Maze. Psychology experiments sometimes involve testing the ability of rats to navigate mazes. The mazes are classified according to difficulty, as measured by the mean length of time it takes rats to find the food at the end. One researcher needs a maze that will take rats an average of about one minute to solve. He tests one maze on several rats, collecting the data shown.

1. Plot the data. Do you think the conditions for inference are satisfied?
   Explain.
2. Test the hypothesis that the mean completion time for this maze is 60 seconds. What is your conclusion?
3. Eliminate the outlier, and test the hypothesis again. What is your conclusion?
4. Do you think this maze meets the "one-minute average" requirement? Explain.

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