Rock band The Rolling Stones have played scores of concerts in the last twenty years. For...

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 2.19 million dollars.

Part a) Assuming a population standard deviation gross earnings of 0.48 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: ( , ).

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 2.19

Population standard deviation = = 0.48

Sample size = n =30

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Margin of error = E = Z_/2* ( / $\sqrt$ n)

= 2.576* (0.48 / $\sqrt$ 30)

= 0.226

At 99% confidence interval estimate of the population mean is,

- E < < + E

2.19 - 0.226 < < 2.19 +0.226

1.964< < 2.416

(1.964 , 2.416 )

orchestra answered 1 year ago

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