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?

Answer 1

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)

μ = M ± Z(s_M)

s_M = standard error = √(s²/n)

M = 28500
z = 1.28
s_M = √(3500²/75) = 404.15
μ = M ± Z(s_M)
μ = 28500 ± 1.28*404.15
μ = 28500 ± 517.93

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

80% CI [27982.07, 29017.93].

c)

s_M = 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

answered by: anonymous