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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).

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

You are testing H0:渭=10against Ha:渭<10based on an SRS of20

observations from a Normal population. The t statistic is t=鈭�2.25

The P-value

a. falls between 0.01 and 0.02.

b. falls between 0.02 and 0.04.

c. falls between 0.04 and 0.05.

d. falls between 0.05 and 0.25.

e. is greater than 0.25.

Walking to school Refer to Exercise 36.

a. Explain why the sample result gives some evidence for the alternative hypothesis.

b. Calculate the standardized test statistic and P-value.

c. What conclusion would you make?

More lefties?In the population of people in the United States, about 10% are left-handed. After bumping elbows at lunch with several left-handed students, Simon wondered if more than 10%of students at his school are left-handed. To investigate, he selected an SRS of 50students and found 8lefties (p铃�=8/50=0.16).

To determine if these data provide convincing evidence that more than 10%of the students at Simon鈥檚 school are left-handed, 200trials of a simulation were conducted. Each dot in the graph shows the proportion of students that are left-handed in a random sample of 50students, assuming that each student has a 10%chance of being left handed.

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

b. Use the simulation results to estimate the P-value of the test in part (a). Interpret the P-value.

c. What conclusion would you make?

Fonts and reading ease Does the use of fancy type fonts slow down the reading of text on a computer screen? Adults can read four paragraphs of a certain text in the common Times New Roman font in an average time of 22 seconds. Researchers asked a random sample of 24 adults to read this text in the ornate font named Gigi. Here are their times (in seconds):

Do these data provide convincing evidence that it takes adults longer than 22 seconds, on average, to read these four paragraphs in Gigi font?

Roulette An American roulette wheel has 18red slots among its 38slots. To test if a particular roulette wheel is fair, you spin the wheel 50times and the ball lands in a red slot 31times. The resulting P-value is0.0384.

a. Interpret the P-value.

b. What conclusion would you make at the伪=0.05 level?

c. The casino manager uses your data to produce a99% confidence interval for p and gets(0.44,0.80). He says that this interval provides convincing evidence that the wheel is fair. How do you respond
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