Question

Annual starting salaries for college graduates with degrees in business administration are generally expected to be between 30,000 and 35,000. Assume that a  confidence interval estimate of the population mean annual starting salary is desired.

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

b. How large a sample should be taken if the desired margin of error is 500? Round your answer to next whole number.

170?

110?

c. Would you recommend trying to obtain the 110 margin of error? Explain.
- Select your answer -

Yes, it always better to be more accurate.

No, the sample size would probably be too time consuming and costly.

Answer 1

Maximum = 35000

Minimum = 30000

Range = maximum - minimum = 35000 - 30000 = 5000

Using Range rule of thumb

(a)

Standard deviation = Range / 4 = 5000 / 4 = 1250

(b)

E = 500

At 95%

Z_/2 = Z_0.025 = 1.96

sample size = n = [Z_/2* / E] ²

n = [1.96 * 1250 / 500]²

n = 25

Sample size = n = 25

(c)

Yes

E = 110

sample size = n = [Z_/2* / E] ²

n = [1.96 * 1250 / 110]²

n = 497

Sample size = n = 497

Yes, it always better to be more accurate