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Chapter 9: Q T9.8 (page 616)
In a test ofagainst , a random sample of size 100 yields a standardized test statistic of . Which of the following is closest to the P-value for this test?
a. 0.90
b. 0.40
c. 0.05
d. 0.20
e. 0.10
The correct option is (d) i.e
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Flu vaccine A drug company has developed a new vaccine for preventing the flu. The company claims that fewer than 5% of adults who use its vaccine will get the flu. To test the claim, researchers give the vaccine to a random sample of 1000 adults.
a. State appropriate hypotheses for testing the company鈥檚 claim. Be sure to define your parameter.
b. Describe a Type I error and a Type II error in this setting, and give the consequences Page Number: 615 of each.
c. Would you recommend a significance level of 0.01, 0.05, or 0.10 for this test? Justify your choice.
d. The power of the test to detect the fact that only 3% of adults who use this vaccine would develop flu using 伪=0.05 is 0.9437. Interpret this value.
e. Explain two ways that you could increase the power of the test from part (d).
Don鈥檛 argue Refer to Exercises 2 and 12.
a. What conclusion would you make at the level?
b. Would your conclusion from part (a) change if a significance level was used
instead? Explain your reasoning.
Two-sided test Suppose you want to perform a test of
versus at the significance level. A random sample
of size from the population of interest yields and
. Assume that the conditions for carrying out the test are met.
a. Explain why the sample result gives some evidence for the alternative hypothesis.
b. Calculate the standardized test statistic and P-value.
Interpreting a -value A student performs a test of versus Ha: and gets a -value of The student says, "There is a probability of getting the sample result I did by chance alone." Explain why the student's explanation is wrong.
Better parking A local high school makes a change that should improve student
satisfaction with the parking situation. Before the change, of the school鈥檚 students approved of the parking that was provided. After the change, the principal surveys an SRS of from the more than students at the school. In all, students say that they approve of the new parking arrangement. The principal cites this as evidence that the change was effective.
a. Describe a Type I error and a Type II error in this setting, and give a possible
consequence of each.
b. Is there convincing evidence that the principal鈥檚 claim is true?
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