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 I indicate that s = 7.5 hours.
(a) How many people are needed to estimate the number of hours people watch television per week within 2 hours with 95% confidence?


(b) How many people are needed to estimate the number of hours people watch television per week within 1 hour with 95% confidence?


(c) What effects does doubling the required accuracy have on the sample size?


(d) How many people are needed to estimate the number of hours people watch television per week within 2 hours with 90% confidence? Compare this result to part (a). How does decreasing the level of confidence in the estimate affect sample size? Why is this reasonable?

Answer 1

Answer:

A.) 54 subjects

B.) 216 subjects

C.) doubling the accuracy results in 4 times the sample size

D.) 38 subjects

Decreasing confidence level decreases sample size. For fixed error margin, the lower the confidence level, the lower the sample size

Explanation:

Standard deviation (s) = 7.5 hours

A.)

Error margin 'E' = 2

Confidence level = 0.95

α = 1 - 0.95 = 0.05, α/2 = 0.025

Z - value at α/2 = 0.025 = 1.96

Sample size = [(1.96 × 7.5)/2]^2

Sample size = 7.35^2 = 54.022

54 subjects

B.) E = 1

Sample size = [(1.96 × 7.5)/1]^2

Sample size = 14.7^2 = 216.09

216 subjects

C.) from the above, doubling the accuracy results in 4 times the sample size.

D.) Using a confidence interval of 90%

Error margin 'E' = 2

Confidence level = 0.90

α = 1 - 0.90 = 0.1, α/2 = 0.05

Z - value at α/2 = 0.05 = 1.645

Sample size = [(1.645 × 7.5)/2]^2

Sample size = 6.16875^2 = 38.05

=38 subjects

Decreasing confidence level decreases sample size. For fixed error margin, the lower the confidence level, the lower the sample size