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According to a recent​ survey, the average earnings in a certain city were ​$41 comma 80041,800...

According to a recent​ survey, the average earnings in a certain city were ​$41 comma 80041,800 in Educational Services and ​$77 comma 40077,400 in the Financial Services industry.

​a) Suppose the standard deviation of earnings in Educational Services for the whole of the city was ​$11 comma 20011,200 and we want the standard deviation of average earnings in our survey to be ​$10001000.

What sample size do we need to​ take?

​b) Suppose we used a sample of size 370370 for our estimate of average earnings in Financial Services and the standard deviation of earnings in our survey was ​$19 comma 40019,400.

What is the standard error of the average earnings in Financial​ Services?

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Answer #1

According to a recent​ survey, the average earnings in a certain city were ​$41,800 in Educational Services and ​$77,400 in the Financial Services industry.

​a) Suppose the standard deviation of earnings in Educational Services for the whole of the city was ​$11,200 and we want the standard deviation of average earnings in our survey to be ​$1000.

What sample size do we need to​ take?

​ standard deviation of sample average earnings =sd/sqrt(n)

11200/sqrt(n) =1000

Sqrt(n) = 11200/1000 = 11.2

n=125.44

= 125 ( rounded)

b) Suppose we used a sample of size 370 for our estimate of average earnings in Financial Services and the standard deviation of earnings in our survey was ​$19,400.

What is the standard error of the average earnings in Financial​ Services?

standard error = sd/sqrt(n) = 19400/sqrt(370)

=1008.56

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