You are planning a survey of starting salaries for recent bu

You are planning a survey of starting salaries for recent business majors. In the latest survey by the National Association of Colleges and Employers, the average starting salary was reported to be $55,144. If you assume that the standard deviation is $11,000, what sample size do you need to have a margin of error equal to $1000 with 95% confidence.

Solution

ANSWER:

MOE = zscore * std / (n) ^ 1/2

moe = 1000

std = 11,000

z score with 95% confidence level = 1.96

1000 = 1.96 * 11000 / (n) ^ 1/2

1000 * (n) ^ 1/2 = 21,560

n^1/2 = 21,560 / 1000

n^1/2 = 21.56

squaring both sides we get

n = (21.56) ^ 2

n = 464.83 = 465

so i need 465 people roughly to have a margin of error of $1,000 with 95% confidence.