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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 ofμis(2.0349,2.5051)

Step by step solution

01

Given Information

It is given that

σ=0.5million

n=30

x¯=2.27

02

Determination of Confidence Level

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

Now,

Confidence level for 90%confidence interval of μ=99%=100×0.99%

⇒1-α=0.99

⇒α=0.01

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

03

Determination of 99% confidence interval of μ

It is given by formula

x¯-z0.005×σn,x¯+z0.002×σn

=2.27-2.575×0.530,2.27+2.575×0.530

=2.27-0.2351,2.27+0.2351

=2.0349,2.5051

Therefore,99%confidence interval ofμis2.0349,2.5051

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Most popular questions from this chapter

A variable has a mean of 100 and a standard deviation of 16 Four observations of this variable have a mean of 108 and a sample standard deviation of 12 . Determine the observed value of the

a. standardized version of x¯.

b. studentized version of x¯.

Table IV in Appendix A contains degrees of freedom from I to 75 consecutively but then contains only selected degrees of freedom.

a. Why couldn't we provide entries for all possible degrees of freedom?

b. Why did we construct the table so that consecutive entries appear for smaller degrees of freedom but that only selected entries occur for larger degrees of freedom?

c. If you had only Table IV, what value would you use for t0 os with df =87 with df=125? with df=650? with df=3000 ? Explain your answers.

Explain the effect on the margin of error and hence the effect on the accuracy of estimating a population mean by a sample mean.

Decreasing the sample size while keeping the same confidence level.

State True or False. Give Reasons for your answers.

The confidence level can be determined if you know only the margin of error.

M\&Ms. In the article "Sweetening Statistics-What M\&M's Can Teach Us" (Minitab Inc., August 2008), M. Paret and E. Martz discussed several statistical analyses that they performed on bags of M\&Ms. The authors took a random sample of 30 small bags of peanut M\&Ms and obtained the following weights, in grams (g).

a. Determine a 95%lower confidence bound for the mean weight of all small bags of peanut M\&Ms. (Note: The sample mean and sample standard deviation of the data are 52.040gand 2.807grespectively.)

b. Interpret your result in pant (a).

c. According to the package, each small bag of peanut M\&Ms should weigh 49.3gComment on this specification in view of your answer to part (b) It provides equal confidence with a greater lower limit.

Part (c) Because the weight of 49.3g is below the 95% lower confidence bound.
See all solutions

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