16 A 95 confidence interval for the proportion of Americans

16. A 95% confidence interval for the proportion of Americans under the age of thirty who skip breakfast is found to be (0.2025, 0.2795). For each choice below, answer True or False:

a. T or F There is a 95% probability that the true proportion of Americans under the age of thirty who skip breakfast is between 20.25% and 27.95%.

b. If this study were to be repeated many times with samples of the same size, then 95% of the time the true proportion will be between 0.2025 and 0.2795 on average.

c. T or F We can be 95% confident that, on average, the proportion of Americans under the age of thirty sampled who skip breakfast is between 0.2025 and 0.2795.

d. T or F   We can be 95% confident that, on average, the proportion of Americans under the age of thirty who skip breakfast is between 0.2025 and 0.2795.

e. T or F If were were to construct one hundred confidence intervals, then 95% of them would contain the true proportion of Americans under the age of thirty who skip breakfast, five percent would not.

Solution

a. FALSE
b. FALSE
c. TRUE
D. TRUE
E. FALSE