Question

# Annual starting salaries for college graduates with degrees in business administration are generally expected to be...

Annual starting salaries for college graduates with degrees in
business administration are generally expected to be between \$30,000 and
\$45,000. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired.

a. What is the planning value for the population standard deviation?

How large a sample should be taken if the desired margin of error is
b.\$500?

c.\$200?

d.\$100?

e.Would you recommend trying to obtain the \$100 margin of error? Explain.

a)
std. dev. = (45000 - 30000)/4 = 3750

b)
The following information is provided,
Significance Level, α = 0.05, Margin or Error, E = 500, σ = 3750

The critical value for significance level, α = 0.05 is 1.96.

The following formula is used to compute the minimum sample size required to estimate the population mean μ within the required margin of error:
n >= (zc *σ/E)^2
n = (1.96 * 3750/500)^2
n = 216.09 i.e. 216

c)
n >= (zc *σ/E)^2
n = (1.96 * 3750/200)^2
n = 1350.56 i.e. 1351

d)
n >= (zc *σ/E)^2
n = (1.96 * 3750/100)^2
n = 5402.25 i.e. 5402

e)
No, because the sample size of 5402 is not practical to have.