The department of Labor wants to estimate the amount of an annual base salary ne
ID: 3243055 • Letter: T
Question
The department of Labor wants to estimate the amount of an annual base salary needed for a factory worker in the state of Alabama as part of a new assistance program. In a sample of 250 workers, they found that the average yearly salary needed is $39,550 with a standard deviation of $4,000.
(a) What is the population mean? What is the best estimate of the population mean?
(b) Based on this sample information, develop a 95% confidence interval for the population mean.
(c) Assume a 99% level of confidence. How large of a sample is required with an acceptable error of $500?
SHOW ALL WORK PLEASE
Explanation / Answer
a) best estimate of the population mean=39550
b) std error of mean =std deviation/(n)1/2=252.98
for 95% CI, z=1.96
therefore 95% confidence interval = mean -/+ z*std error =39054.16 ; 40045.84
c)for 99% CI, z=2.5758
margin of error E=500
therefore sample size =(z*std deviation/E)2 =~425