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Chapter 9: Q .6. (page 564)

Ski jump When ski jumpers take off, the distance they fly varies considerably depending on their speed, skill, and wind conditions. Event organizers must position the landing area to allow for differences in the distances that the athletes fly. For a particular competition, the organizers estimate that the variation in distance flown by the athletes will be \(\sigma=10\) \(\sigma=10\) meters. An experienced jumper thinks that the organizers are underestimating the variation.

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01

Step 1:Given information

Ski jump When ski jumpers take off, the distance they fly varies considerably depending on their speed, skill, and wind conditions. Event organizers must position the landing area to allow for differences in the distances that the athletes fly. For a particular competition, the organizers estimate that the variation in distance flown by the athletes will be $\sigma=10$ $\sigma=10$ meters. An experienced jumper thinks that the organizers are underestimating the variation.

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

02

Step 2:Explaination

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Most popular questions from this chapter

Pressing pills Refer to Exercise 77.

a. Construct and interpret a 95% confidence interval for the true hardness μ of the tablets in this batch. Assume that the conditions for inference are met.

b. Explain why the interval in part (a) is consistent with the result of the test in Exercise 77.

No homework? Refer to Exercise 1. The math teachers inspect the

homework assignments from a random sample of 50 students at the school. Only 68% of the students completed their math homework. A significance test yields a P-value of 0.1265.

a. Explain what it would mean for the null hypothesis to be true in this setting.

b. Interpret the P-value.

Losing weight A Gallup poll found that 59% of the people in its sample said “Yes” when asked, “Would you like to lose weight?” Gallup announced: “For results based on the total sample of national adults, one can say with 95% confidence that the margin of (sampling) error is ±3 ±3percentage points.”12 Based on the confidence interval, is there convincing evidence that the true proportion of U.S. adults who would say they want to lose weight differs from 0.55? Explain your reasoning

Upscale restaurant You are thinking about opening a restaurant and are searching for a good location. From the research you have done, you know that the mean income of those living near the restaurant must be over \(85,000to support the type of upscale restaurant you wish to open. You decide to take a simple random sample of 50people living near one potential site. Based on the mean income of this sample, you will perform a test at the

α=0.05 significance level of H0:μ=\)85,000versus Ha:μ>\(85,000, where μ is the true mean income in the population of people who live near the restaurant. The power of the test to detect that μ=\)86,000is 0.64 Interpret this value.

No homework? Mr. Tabor believes that less than 75%of the students at his school completed their math homework last night. The math teachers inspect the homework assignments from a random sample of 50 students at the school.
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