Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $10,000 and $35,000. 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.
Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $10,000 and $35,000. | |||||||||||
Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. | |||||||||||
How large a sample should be taken for each desired margin of error below? | |||||||||||
Starting Salary | Desired margin of error | ||||||||||
Lower | 10000 | 400 | |||||||||
Upper | 35000 | ||||||||||
250 | |||||||||||
100 |
For a margin of error of ± $400 , the required sample size is n =
For a margin of error of ± $250 , the required sample size is n =
For a margin of error of ± $100 , the required sample size is n =
Would you recommend trying to obtain the $100 margin of error? Explain.
estimated standard deviation =range/4 =(35000-10000)/4=6250
a)
for95% CI crtiical Z = | 1.96 |
margin of error E = | 400 | |
required sample size n=(zσ/E)^{2 } = | 938 |
b)
required sample size n=(zσ/E)^{2 } = | 2401 |
c)
required sample size n=(zσ/E)^{2 } = | 15006 |
d)since 15006 sample size is very high and will cost a lot , $100 margin of error is not recommended
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