How many should be surveyed?

Question

A survey is prepared to determine how much a selected portion of the population watches Television. A pilot survey indicates the mean time per week is 12 hours with a standard deviation of 3 hours. It is desired to estimate the mean viewing time within 15 minutes. Using a level of confidence of 95%, how many people of the selected portion should be surveyed?

Answer 1

mean = 12hr

std dev = 3hr

margin of error = 15min = 0.25hr

CI = 95%

 

Based on the information given in the problem, you are not given the population standard deviation, so you will use t-values. The critical t value associated with a 95% confidence interval is 1.96

 

Margin of Error = (critical t value) x [standard deviation/sqrt(sample size)]

0.25 = 1.96 x [3/sqrt(n)]

0.25sqrt(n) = 5.88

sqrt(n) = 23.52

n = (23.52)^2

n = 553.19

n = 554 <-- you cannot have a partial person, so always round up