Question

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. Given the information in the Microsoft Excel Online file below, construct a spreadsheet to determine how large a sample should be taken for each desired margin of error.

1. For a margin of error of ± $400 , the required sample size is n =

2. For a margin of error of ± $170 , the required sample size is n =

3. For a margin of error of ± $100 , the required sample size is n =

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

   _________Yes, it always better to be more accurate.No, the sample size would probably be too time consuming and costly.

Answer 1

here from range rule of thumb; std deviation =range/4 =(45000-30000)/4 =3750

a)

for 95 % CI value of z=	1.960
standard deviation σ=	3750
margin of error E =	400
required sample size n=(zσ/E)2                                         =	338.0

b)

for 95 % CI value of z=	1.960
standard deviation σ=	3750
margin of error E =	170
required sample size n=(zσ/E)2                                         =	1870.0

c)

for 95 % CI value of z=	1.960
standard deviation σ=	3750
margin of error E =	100
required sample size n=(zσ/E)2                                         =	5403.0

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