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The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset Vaia Explanations$ Math

6th Edition · 837 pages

ISBN: 9781319113339

Chapter 9: Q R9.5 (page 615)

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’s 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 α=0.05 is 0.9437. Interpret this value.
e. Explain two ways that you could increase the power of the test from part (d).

Short Answer

Expert verified

Part a)

Part b)

Part c)

Part d)

Part e)

Step by step solution

01

Part (a) Step 1:Given information

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Most popular questions from this chapter

Side effects A drug manufacturer claims that less than $10 %$ of patients who take its new drug for treating Alzheimer’s disease will experience nausea. To test this claim, researchers conduct an experiment. They give the new drug to a random sample of $300$ out of $5000$ Alzheimer’s patients whose families have given informed consent for the patients to participate in the study. In all, $25$ of the subjects experience nausea.

a. Describe a Type I error and a Type II error in this setting, and give a possible

consequence of each.

b. Do these data provide convincing evidence for the drug manufacturer’s claim?

A significance test allows you to reject a null hypothesis $H 0 H_{0}$ in favor of an alternative hypothesis ${Ha}_{a}$ at the $5 %$ significance level. What can you say about significance at the $1 %$ level?

a. $H 0 H_{0}$ can be rejected at the $1 %$ significance level.

b. There is insufficient evidence to reject $H_{0} H_{0}$ at the $1 %$ significance level.

c. There is sufficient evidence to accept $H_{0} H_{0}$ at the $1 %$ significance level.

d. ${Ha}^{H_{a}}$ can be rejected at the $1 %$ significance level.

e. The answer can't be determined from the information given.

Based on the $P$ -value in Exercise 31, which of the following would be the most

appropriate conclusion?

a. Because the P-value is large, we reject $H_{0}$ . We have convincing evidence that more than $50 %$ of city residents support the tax increase.

b. Because the $P$ -value is large, we fail to reject $H_{0}$ . We have convincing evidence that more than $50 %$ of city residents support the tax increase.

c. Because the $P$ -value is large, we reject $H_{0}$ . We have convincing evidence that at most $50 %$ of city residents support the tax increase.

d. Because the $P$ -value is large, we fail to reject $H_{0}$ . We have convincing evidence that at most $50 %$ of city residents support the tax increase.

e. Because the $P$ -value is large, we fail to reject $H_{0}$ . We do not have convincing

evidence that more than $50 %$ of city residents support the tax increase.

How much juice? One company's bottles of grapefruit juice are filled by a machine that is set to dispense an average of $180$ milliliters (ml) of liquid. A quality-control inspector must check that the machine is working properly. The inspector takes a random sample of $40$ bottles and measures the volume of liquid in each bottle.

state appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest

AttitudesThe Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students' attitudes toward school and study habits. Scores range from 0 to 200 . Higher scores indicate better attitudes and study habits. The mean score for U.S. college students is about 115. A teacher suspects that older students have better attitudes toward school, on average. She gives the SSHA to an SRS of 45 of the over 1000 students at her college who are at least 30 years of age.

state appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest

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