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Chapter 9: Q.18 (page 547)
Write a few sentences comparing what the P-values in Exercises 13 and 14 tell you about statistical significance in each of the two studies.
For P-value in exercisethe convincing evidence is stronger
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Growing tomatoes An agricultural field trial compares the yield of two varieties of tomatoes for commercial use. Researchers randomly selected Variety A and Variety B tomato plants. Then the researchers divide in half each small plots of land in different locations. For each plot, a coin toss determines which half of the plot gets a Variety A plant; a Variety B plant goes in the other half. After harvest, they compare the yield in pounds for the plants at each location. The differences give and. A graph of the differences looks roughly symmetric and single-peaked with no outliers. Is there convincing evidence that Variety A has a higher mean yield? Perform a significance test using to answer the question.
Improving health A large company's medical director launches a health promotion campaign to encourage employees to exercise more and eat better foods. One measure of the effectiveness of such a program is a drop in blood pressure. The director chooses a random sample of employees and compares their blood pressures from physical cams given before the campaign and again a year later. The mean change (after - before) in systolic blood pressure for these employees is and the standard deviation is .
(a) Do these data provide convincing evidence of an average decrease in blood pressure among all of the company's employees during this year? Carry out a test at the significance level.
(b) Can we conclude that the health campaign caused a decrease in blood pressure? Why or why not?
In planning a study of the birth weights of babies whose mothers did not see a doctor
before delivery, a researcher states the hypotheses as
Spinning for apples (6,3 or 7.3) In the "Ask Marilyn" column of Parade magzine, a reader posed this question: "Say that a slot machine has five wheels, and each wheel has five symbols: an apple, a grape, a peach, a pear, and a plum. I pull the lever five times. What are the chances that I'll get at least one apple?" Suppose that the wheels spin independently and that the fre symbols are equally likely to appear on each wheel in a given spin.
(a) Find the probability that the slot player gets at least one apple in one pull of the lever. Show your method clearly.
(b) Now answer the reader's question. Show your method clearly.
One-sided test Suppose you carry out a significance test of versus based on a sample of size and obtain .
(a) Find the P-value for this test using (i) Table and (ii) your calculator. What conclusion would you draw at the significance level? At the significance level?
(b) Redo part (a) using an alternative hypothesis of.
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