It is the contract negotiation time, & the LA teachers union wants to argue that

Question

It is the contract negotiation time, & the LA teachers union wants to argue that its salaries are the lowest in the region. Because the union has 20,000 members, it must rely on a survey. If the union wants to estimate its members' mean salary & be 95% sure that the estimate is within $200 of the real mean, how large a sample should the union use? Assume that a preliminary survey estimates the mean as $35,000, with a $1,000 standard deviation.

I know the answer is 96 but I'd like to know the steps in finding out that answer. Thanks.

It is the contract negotiation time, & the LA teachers union wants to argue that its salaries are the lowest in the region. Because the union has 20,000 members, it must rely on a survey. If the union wants to estimate its members' mean salary & be 95% sure that the estimate is within $200 of the real mean, how large a sample should the union use? Assume that a preliminary survey estimates the mean as $35,000, with a $1,000 standard deviation.

I know the answer is 96 but I'd like to know the steps in finding out that answer. Thanks.

Explanation / Answer

Margin of error <200

Z alpha/2 for 95% = 1.96

Hence std error = 200/1.96 = 102.041

Std dev/ rtn <102.041

i.e. 1000/rtn <102.041

rtn >1000/102.041=9.8

n>96.04

Hence n should be atleast 97.

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