4. The department of finance of Wells Fargo Bank wants to estimate the amount of

Question

4. The department of finance of Wells Fargo Bank wants to estimate the amount of an annual healthcare premium needed for an investor banker as part of a new recruiting program. In a sample of 75 investor bankers, they found that the average yearly premium needed is $28,500 with a standard deviation of $3,500. (a) What is the population mean? What is the best estimate of the population mean? (b) Develop an 80% confidence interval for the population mean. (c) Assuming a 99% level of confidence, how large of a sample is required with an acceptable error of $300?

Explanation / Answer

A) As the sample is of 75 investors we can assume that it follows the normal distribution with the population means equal to sample mean of 28,500.

b)

= M ± Z(sM)

sM = standard error = (s2/n)

M = 28500
z = 1.28
sM = (35002/75) = 404.15
= M ± Z(sM)
= 28500 ± 1.28*404.15
= 28500 ± 517.93

You can be 80% confident that the population mean () falls between 27982.07 and 29017.93.

80% CI [27982.07, 29017.93].

c)

sM = standard error = (s2/n)

3002=s2/n

n = 35002 /3002=12250000/90000=136.11

A sample of 137 is required with an acceptable error of 300

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