Annual starting salaries of college graduates with degrees in business administr

Question

Annual starting salaries of college graduates with degrees in business administration are generally expected to be between $30,000 and $45,000. 1) Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. Determine the planning value for the population standard deviation. 2) Determine how large a sample should be taken if the desired margin of error is

: a. $500 b. $200 c. $100 d. Would you recommend trying to obtain the $100 margin of error?

Explain, I know you divide by 4 but i need to know why

Explanation / Answer

(1) the planning value for the population standard deviation = (45000-30000)/4 =3750

The assumption of range/4 leads to a larger planning estimate for the std dev, and thus is more conservative (leads to larger sample size needed) - so I think range/4 is to be preferred here.

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

(a) n=(Z*s/E)^2

=(1.96*3750/500)^2
=216.09

Take n=217

(b)n=(Z*s/E)^2

=(1.96*3750/200)^2
=1350.562

Take n=1351

(c) n=(Z*s/E)^2

=(1.96*3750/100)^2

=5402.25

Take n=5403

(d) no, because the sample size is too larger.

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