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Chapter 9: Q.8 (page 598)
In a test of against , a random sample of size yields a test statistic of . The P-value of the test is approximately equal to
(a) .
(b) .
(c) .
(d) .
(e) .
The correct answer is (d) 0.20.
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A Gallup Poll report on a national survey of 1028 teenagers revealed that 72% of teens said they seldom or never argue with their friends. Yvonne wonders whether this national result would be true in her large high school. So she surveys a
a random sample of 150 students at her school.
The power of tomatoes The researchers who carried out the experiment in Exercise suspect that the large P-value () is due to low power.
(a) Describe a Type I and a Type II error in this setting. Which type of error could you have made in Exercise ? Why?
(b) Explain two ways that the researchers could have increased the power of the test to detect .
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 text in the common Times New Roman font in an average time of seconds. Researchers asked a random sample of adults to read this text in the omate font named Gigi. Here are their times, in seconds:
| 23.2 | 21.2 | 28.9 | 27.7 | 29.1 | 27.3 | 16.1 | 22.6 | 25.6 | 34.2 | 23.9 | 26.8 |
| 20.5 | 34.3 | 21.4 | 32.6 | 26.2 | 34.1 | 31.5 | 24.6 | 23.0 | 28.6 | 24.4 | 28.1 |
Do these data provide good evidence that the mean reading time for Gigi is greater than seconds? Carry out an appropriate test to help you answer this question.
- Use a confidence interval to draw a conclusion for a two-sided test about a population mean.
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.
Flu vaccine A drug company has developed a new vaccine for preventing the flu. The company claims that fewer than of adults who use its vaccine will get the flu. To test the claim, researchers give the vaccine to a random sample of adults. Of these, get the flu.
(a) Do these data provide convincing evidence to support the company's claim? Perform an appropriate test to support your answer.
(b) Which kind of mistake - a Type I error or a Type II error-could you have made in (a)? Explain.
(c) From the company's point of view, would a Type I error or Type Il error be more serious? Why?
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