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Chapter 8: Q 8.74 (page 332)

Keep on Rolling. The Rolling Stones, a rock group formed in the 1960s, have toured extensively in support of new albums, Pollstar has collected data on the earnings from the Stones's North American tours. For thirty randomly selected Rolling Stones concerts, the mean gross earnings is \(2.27 million. Assuming a population standard deviation gross earnings of \)0.5 million, obtain a 99% confidence interval for the mean gross earnings of all Rolling Stones concerts. Interpret your answer in words.

Short Answer

Expert verified

99%confidence level of渭is(2.0349,2.5051)

Step by step solution

01

Given Information

It is given that

蟽=0.5million

n=30

x炉=2.27

02

Determination of Confidence Level

It is given that sample mean earning is x炉=2.27

Now,

Confidence level for 90%confidence interval of 渭=99%=100脳0.99%

鈬�1-伪=0.99

鈬�伪=0.01

Hence,za2=z0.012=z0.005=2.575

03

Determination of 99% confidence interval of μ

It is given by formula

x炉-z0.005脳蟽n,x炉+z0.002脳蟽n

=2.27-2.575脳0.530,2.27+2.575脳0.530

=2.27-0.2351,2.27+0.2351

=2.0349,2.5051

Therefore,99%confidence interval of渭is2.0349,2.5051

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Most popular questions from this chapter

In each Exercises 8.11-8.16, we provide a sample mean, sample size, and population standard deviation. In each case, perform the following Lacks.

a. Find a 95%confidence interval for the population mean. (Note: You may want to review Example 8.2, which begins on the page 316)

b. Identify and interpret the margin of error.

c. Express the endpoints of the confidence interval in terms of the point estimate and the margin of error.

x^=35,n=25,蟽=4

Suppose that you take500 simple random samples from a population and that, for each sample, you obtain a 90%confidence interval for an unknown parameter. Approximately how many of those confidence intervals will not contain the value of the unknown parameter?

Two t-curves have degrees of freedom 12 and 20 , respectively. Which one more closely resembles the standard normal curve? Explain your answer.

Assume that the population standard deviation is known and decide weather use of the zinterval procedure to obtain a confidence interval for the population mean is reasonable. Explain your answers.

The variable under consideration is very close to being normally distributed, and the sample size is75.

Cottonmouth Litter Size. In the article "The Eastern Cottonmouth (Agkistrodon piscivorus) at the Northern Edge of Its Range" (Journal of Herpetology, Vol. 29 No. 3 pp. 391-398), C. Blem and L. Blem examined the reproductive characteristics of the eastern cottonmouth, a once widely distributed snake whose numbers have decreased recently due to encroachment by humans. A simple random sample of 44 female cottonmouths yielded the following data on the number of young per litter.

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b. Is your point estimate in part (a) likely to equal 渭 exactly? Explain your answer.
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