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Chapter 9: Q 107. (page 611)

Vigorous exercise helps people live several years longer (on average). Whether mild activities like slow walking extend life is not clear. Suppose that the added life expectancy from regular slow walking is just 2 months. A significance test is more likely to find a significant increase in mean life expectancy with regular slow walking if

Step 2: Explanation

Short Answer

Expert verified

The correct option is (a).

Step by step solution

01

Given information

a. It uses a 5% significance level and is based on a very large random sample.

b. It is based on a very large random sample with a significance level of one percent.

c. It uses a 5% significance level and is based on a very small random sample.

d. It is based on a very small random sample with a significance level of one percent.

e. The number of people in the sample has no bearing on the test's significance.

02

Explanation

"It is based on a very big random sample and a significance level is applied," is the best response to the supplied statement.

There will be a difference in the mean life expectancy between individuals who perform strenuous exercise and those who do regular slow-walking since vigorous exercise leads to living several months longer on average and regular slow-walking leads to living months longer on average.

The higher the sample size, the more data regarding the difference in life expectancy will be available, and the more valid the estimates will be. However, because there is a difference in mean life expectancy, one will very certainly reject the null hypothesis, implying that a considerable increase is more plausible. So the correct option is (a).

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Most popular questions from this chapter

Candy! A machine is supposed to fill bags with an average of 19.2 ounces of candy. The manager of the candy factory wants to be sure that the machine does not consistently underfill or overfill the bags. So the manager plans to conduct a significance test at the 伪=0.10significance level of

H0:渭=19.2Ha:渭notequalto19.2

where 渭=the true mean amount of candy (in ounces) that the machine put in all bags filled that day. The manager takes a random sample of 75 bags of candy produced that day and weighs each bag. Check if the conditions for performing the test are met.

Bags of a certain brand of tortilla chips claim to have a net weight of 14ounces. Net weights vary slightly from bag to bag and are Normally distributed with mean 渭 . A representative of a consumer advocacy group wishes to see if there is convincing evidence that the mean net weight is less than advertised and so intends to test the hypotheses

H0:渭=14Ha:渭<14

A Type I error in this situation would mean concluding that the bags

a. are being underfilled when they aren鈥檛.

b. are being underfilled when they are.

c. are not being underfilled when they are.

d. are not being underfilled when they aren鈥檛.

e. are being overfilled when they are underfilled

Restaurant power Refer to Exercise 86 Determine if each of the following changes would increase or decrease the power of the test. Explain your answers.

a. Use a random sample of 30 people instead of 50 people.

b. Try to detect that 渭=\(85,500 instead of 渭=\)86,000

c. Change the significance level to 伪=0.10

Home computers Jason reads a report that says 80%of U.S. high school

students have a computer at home. He believes the proportion is smaller than 0.80at his large rural high school. Jason chooses an SRS of 60students and finds that 41have a computer at home. He would like to carry out a test at the 伪=0.05significance level of H0:p=0.80versus Ha:p<0.80, where p= the true

proportion of all students at Jason鈥檚 high school who have a computer at home. Check if the conditions for performing the significance test are met.

Heavy bread? The mean weight of loaves of bread produced at the bakery where you work is supposed to be 1pound. You are the supervisor of quality control at the bakery, and you are concerned that new employees are producing loaves that are too light. Suppose you weigh an SRS of bread loaves and find that the mean weight is 0.975pound.

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

b. Explain why there is some evidence for the alternative hypothesis.

c. The P-value for the test in part (a) is 0.0806. Interpret the P-value.

d. What conclusion would you make at the 伪=0.01 significance level?
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