Can you please help with this question? Thank you!
You want to determine the average number of hours worked by professors at your university per week. You want to be able to express your answer as a confidence interval, with 95% confidence (that is, use z = 1.96) and you are aiming for a precision of plus or minus two hours. Past studies of this type suggest that the variance in professor work hours is about 100 (that is, ?² = 100).
a. How big is the minimum required sample size that would allow you to meet your confidence and precision goals?
b. If you wanted your precision to double (that is, your precision would be plus or minus one hour), how does that affect your minimum required sample size?
c. If you wanted your confidence to increase to 99% (That is, use z = 2.575 instead of 1.96), how does that affect your minimum required sample size?