Question

Annual starting salaries for college graduates with degrees in business administration are generally expected to be between and . 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 ? Round your answers to next whole number. ? ? c. Would you recommend trying to obtain the margin of error? Explain.

Answer 1

Because of the very huge sample size, we do not advise attempting to acquire the $100 margin of error.

The annual starting salaries for college graduates with degrees are between $30,000 and $45,000.

The confidence interval is 95%.

The planning value of the population standard deviation is expressed as:

= ( 45000 - 30000 ) / 4

= 15000/4

= 3750

And, 95% confidence interval a is 0.05.

Using the standard normal table,

Z(0.025) = 1.96

(a) For error E = $500,

n = ( Z × S/E )²

n = ( 1.96 × 3750/500)²

n = 216.09 = 217

(b) For error E = $200,

n = ( Z × S/E )²

n = ( 1.96 × 3750/200)²

n = 1351

(c) For error E = $100

n = ( Z × S/E )²

n = ( 1.96 × 3750/100)²

n = 5403

Therefore, Due to the sample size being too huge, we do not advise attempting to achieve the $100 margin of error.

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