## A report on consumer financial literacy summarized data from a representative sample of 1,664 adult Americans. Based on data from this sampl

A report on consumer financial literacy summarized data from a representative sample of 1,664 adult Americans. Based on data from this sample, it was reported that over half of U.S. adults would give themselves a grade of A or B on their knowledge of personal finance. This statement was based on observing that 939 people in the sample would have given themselves a grade of A or B.

(a) Construct and interpret a 95% confidence interval for the proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance. (Round your answers to three decimal places.)

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(b) Is the confidence interval from part (a) consistent with the statement that a majority of adult Americans would give themselves a grade of A or B? Explain why or why not.

Because this confidence interval _____ is entirely below 0.5contains 0.5is entirely above 0.5 , the interval ______ is not consistent with the statement that a majority of adult Americans would give themselves a grade of A or B.

## Answers ( )

Answer:a.The 95% confidence interval for the proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is (0.54, 0.588). This means that we are 95% sure that the true proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is between these two bounds.b.Because this confidence intervalis entirely above 0.5,the intervalis consistentwith the statement that a majority of adult Americans would give themselves a grade of A or B.Step-by-step explanation:In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following

confidence interval of proportions.In whichz is the zscore that has a pvalue of .

Sample of 1,664 adult Americans, 939 people in the sample would have given themselves a grade of A or B in personal finance.This means that

95% confidence levelSo , z is the value of Z that has a pvalue of , so .

The lower limit of this interval is:The upper limit of this interval is:The 95% confidence interval for the proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is (0.54, 0.588). This means that we are 95% sure that the true proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is between these two bounds.

(b) Is the confidence interval from part (a) consistent with the statement that a majority of adult Americans would give themselves a grade of A or B?Yes, because the confidence interval is entirely above 0.5.

Because this confidence interval

is entirely above 0.5,the intervalis consistentwith the statement that a majority of adult Americans would give themselves a grade of A or B.