Rock band The Rolling Stones have played scores of concerts in the last twenty y

Question

Rock band The Rolling Stones have played scores of concerts in the last twenty years. For 30 randomly selected Rolling Stones concerts, the mean gross earnings is 2.03 million dollars. Part a) Assuming a population standard deviation gross earnings of 0.51 million dollars, obtain a 99% confidence interval for the mean gross earnings of all Rolling Stones concerts (in millions). Please carry at least three decimal places in intermediate steps. Give your answer to the nearest 3 decimal places. Confidence interval: (, ). Part b) Which of the following is the correct interpretation for your answer in part (a)? A. There is a 99% chance that the mean gross earnings of all Rolling Stones concerts lies in the interval B. If we repeat the study many times, 99% of the calculated confidence intervals will contain the mean gross earning of all Rolling Stones concerts. C. We can be 99% confident that the mean gross earnings for this sample of 30 Rolling Stones concerts lies in the interval D. None of the above

Explanation / Answer

The statistical software output for this problem is:

One sample Z confidence interval:
: Mean of population
Standard deviation = 0.51

99% confidence interval results:

Hence,

99% confidence interval will be:

(1.790, 2.270)

Part - b: Options A and B are correct.

Mean n Sample Mean Std. Err. L. Limit U. Limit 30 2.03 0.093112835 1.7901572 2.2698428

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