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Chapter 7: Q. 16 (page 456)

Even more tall girls, Refer to Exercises 12and 14. Suppose that the sample mean height of the twenty 16-year-old females is x=65.8inches. Would this sample mean provide convincing evidence that the average height of all 16-year-old females at this school is greater than 64inches? Explain your reasoning.

Short Answer

Expert verified

It would be remarkable to acquire a sample mean of x=65.8or larger in an SRS of size 20from a normal population with 渭=64inches, because none of the values of xwere 65.8 inches or greater. As a result, a sample mean of x=65.8inches provides convincing evidence

Step by step solution

01

Given information 

We have been given that the sample mean height of the twenty 16-year-old females is x=65.8inches.

02

Explanation

It would be remarkable to acquire a sample mean of x=65.8or larger in an SRS of size 20from a normal population with 渭=64inches and 蟽=2.5inches, because none of the values of xwere 65.8inches or greater. As a result, a sample mean of x=65.8inches provides convincing evidence that the 16-year-old females population mean height is more than 64inches. The disparity between the sample mean (x=65.8) and the mean indicated by the National Center for Health Statistics (渭=64) cannot be explained by sampling variability.

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Most popular questions from this chapter

When people order books from a popular online source, they are shipped in boxes.

Suppose that the mean weight of the boxes is 1.5 pounds with a standard deviation of 0.3 pound, the mean weight of the packing material is 0.5pound with a standard deviation of 0.1 pound, and the mean weight of the books shipped is 12 pounds with a standard deviation of 3 pounds. Assuming that the weights are independent, what is the standard deviation of the total weight of the boxes that are shipped from this source?

a. 1.84

b. 2.60

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d. 3.40

e. 9.10

10%Why is it important to check the 10 % condition before calculating probabilities involving localid="1654670795605">x-?

a. To reduce the variability of the sampling distribution of x-x炉

b. To ensure that the distribution of x-x炉is approximately Normal

c. To ensure that we can generalize the results to a larger population

d. To ensure that x-x炉will be an unbiased estimator of 渭

e. To ensure that the observations in the sample are close to independent

A researcher initially plans to take an SRS of size 160 from a certain population and calculate the sample mean x-x炉. Later, the researcher decides to increase the sample size so that the standard deviation of the sampling distribution of x-x炉will be half as big as when using a sample size of 160 . What sample size should the researcher use?

a. 40

b. 80

c. 320

d. 640

e. There is not enough information to determine the sample size.

An insurance company claims that in the entire population of homeowners, the mean annual loss from fire is and the standard deviation of the loss is 蟽=\(5000.The distribution of losses is strongly right-skewed: many policies have \)0loss, but a few have large losses. The company hopes to sell 1000 of these policies for \(300each.

a. Assuming that the company鈥檚 claim is true, what is the probability that the mean loss from fire is greater than \)300for an SRS of 1000 homeowners?

b. If the company wants to be 90% certain that the mean loss from fire in an SRS of 1000 homeowners is less than the amount it charges for the policy, how much should the company charge?

According to government data, 22%of American children under the age of 6 live in households with incomes less than the official poverty level. A study of learning in

early childhood chooses an SRS of300 children from one state and finds that p鈭�p^=.

a. Find the probability that at least 29%of the sample are from poverty-level households0.29households.

b. Based on your answer to part (a), is there convincing evidence that the percentage of children under the age of 6 living in households with incomes less than the official poverty level in this state is greater than the national value of 22%? Explain your reasoning.
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