Question

A researcher wanted to determine the mean number of hours per week (Sunday through Saturday) the typical person watches television. Results from the Sullivan Statistics Survey indicate that s = 6.5 hours.

a) What is the minimum number of people the researcher must sample if they wish to estimate the mean number of hours to within 2 hours with 95% confidence? n=

b) What is the minimum number of people the researcher must sample if they wish to estimate the mean number of hours to within half an hour with 95% confidence? n=

c) What is the minimum number of people the researcher must sample if they wish to estimate the mean number of hours to within half an hour with 99% confidence? n=

Answer 1

a)
The following information is provided,
Significance Level, α = 0.05, Margin or Error, E = 2, σ = 6.5

The critical value for significance level, α = 0.05 is 1.96.

The following formula is used to compute the minimum sample size required to estimate the population mean μ within the required margin of error:
n >= (zc *σ/E)^2
n = (1.96 * 6.5/2)^2
n = 40.58

sample size = 41

b)
n >= (zc *σ/E)^2
n = (1.96 * 6.5/0.5)^2
n = 649.23

sample size = 650

c)
The critical value for significance level, α = 0.01 is 2.576.

The following formula is used to compute the minimum sample size required to estimate the population mean μ within the required margin of error:
n >= (zc *σ/E)^2
n = (2.576 * 6.5/0.5)^2
n = 1121.45

sample size = 1122