Question

Annual starting salaries for college graduates with degrees in business administration are generally expected to be between 30000 and 50000. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. 1. What is the planning value for the population standard deviation?2. How large a sample should be taken if the desired margin of error is
a. $500?
b. $200?
c. $100?
3. Would you recommend trying to obtain the $100 margin of error? Explain.

Answer 1

Answer:

(1) The planning value for the population standard deviation:

$=\frac{50,000-30,000}{4}$

= 5,000

(2) Given a = 0.05, Z(0.025) = 1.96 (from standard normal table)

$n = (\frac{Z\times SD}{Error}) ^{2}$

(a)

$n = (\frac{1.96\times 5,000}{500}) ^{2}$

n = 384.16

(b)

$n = (\frac{1.96\times 5,000}{200}) ^{2}$

n = 2,401

(c)

$n = (\frac{1.96\times 5,000}{100}) ^{2}$

n = 9,604

(3) No, because the sample size of the study is too larger.