16. A 95% confidence interval for the proportion of Americans under the age of thirty who skip break- fast 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%. F 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. b. T or e. T or F If we 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 break- fast, five percent would not.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 22PFA
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Is 95% confidence means 95% probability to happen? 

### Confidence Interval for Proportion of Americans Skipping Breakfast

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. **T or F** 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 we 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.
Transcribed Image Text:### Confidence Interval for Proportion of Americans Skipping Breakfast 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. **T or F** 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 we 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.
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