Television A researcher wanted to determine the mean number of hours per week (S

Question

Television 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 = 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 effect 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?

Explanation / Answer

s = 7.5

a.) E = 2

1 - = 0.95

= 0.05

/2 = 0.025

z/2 = 1.96

n = [z/2*s / E]2 = 54.02 ~ 54

b) E = 1

1 - = 0.95

= 0.05

/2 = 0.025

z/2 = 1.96

n = [z/2*s / E]2 = 216.09 ~ 216

c) Doubling the accuracy increases the sample size 4 times.

d)

E = 2

1 - = 0.90

= 0.1

/2 = 0.05

z/2 = 1.645

n = [z/2*s / E]2 = 38.05 ~ 38

Decreasing the level of confidence decreases the sample size and this is reasonable because you need more number of people to predict something about more accurately and vice versa.

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