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?

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

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