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a) For 30 randomly selected Rolling Stones concerts, the mean gross earnings is 2.79 million dollars. Assuming a population standard deviation gross earnings of 0.47 million dollars, obtain a 99% confidence interval for the mean gross earnings of all Rolling Stones concerts (in millions). Confidence interval: ( __________________ , __________________ )

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Answer:

The 99% confidence interval for the mean gross earnings of all Rolling Stones concerts (in millions) is (2.5690, 3.0110).

Explanation:

We have that to find our
\alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:


\alpha = (1-0.99)/(2) = 0.005

Now, we have to find z in the Ztable as such z has a pvalue of
1-\alpha.

So it is z with a pvalue of
1-0.005 = 0.995, so
z = 2.575

Now, find M as such


M = z*(\sigma)/(√(n))

In which
\sigma is the standard deviation of the population and n is the size of the sample.


M = 2.575*(0.47)/(√(30)) = 0.2210

The lower end of the interval is the mean subtracted by M. So it is 2.79 - 0.2210 = 2.5690 million dollars.

The upper end of the interval is the mean added to M. So it is So it is 2.79 + 0.2210 = 3.0110 million dollars.

The 99% confidence interval for the mean gross earnings of all Rolling Stones concerts (in millions) is (2.5690, 3.0110).

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