Question

A management consulting firm wishes to estimate the average wage earned by workers in a certain industry. The firm wants the maximum error on the estimate to not exceed $2. It is assumed that the population standard deviation is $10. If the cost of interviewing each worker is $5.00, and the total budget for the study is $500, what level of confidence should be used‐‐ 95% or 98%?

I am not sure how to approach this. Please show working:) Thank you

Answer 1

It says budget for study is $500 and cost to interview each worker is $5

So, maximum sample size allowed = 500/5 = 100

So, we find sample size for each confidence level. Whatever will comes under sample size 100 (within budget of firm) we will use it. If both comes within limit then we will use 98% because that's better than 95%.

When 95% then z = 1.96

Hence, sample size = 97 when CI = 95%.

When 98% then z = 2.33

Hence, sample size = 136 when CI = 98%.

So, we need to take 95% confidence level because that sample size is within budget of the firm.

Please comment if any doubt. Thank you.