Question

In: Statistics and Probability

4. The department of HR at the University of Michigan wants to estimate the amount of...

4. The department of HR at the University of Michigan wants to estimate the amount of an annual healthcare premium needed for an Assistant Professor as part of a new recruiting program. In a sample of 50 Assistant Professors, they found that the average yearly premium needed is $16,000 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 90% 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 $400?

Solutions

Expert Solution

a) Here we dont know population mean we use sample mean and confidence interval to estimante range of population mean, best estimate of population mean is 16000.

b) x?= 16000

sigma= 3500

n= 50

alpha=0.1 then Z(alpha/2)= 1.645

Margin of error E=Z(alpha/2)*sigma/sqrt(n)

=1.645*3500/sqrt(50)

=814.233

90% Confidence interval for population mean =(x?-E,x?+E)

lower bound= 15185.76654

upper bound= 16814.23346

c)

sigma= 3500

MOE= 400

Zalpha/2= 2.576

we know the relation,

E=Z(alpha/2)*sigma/sqrt(n)

400=2.576*3500/sqrt(n)

n= 508.0516

n= 509

.................................................

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