Mathematics, 19.03.2021 15:40 bry7474

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.)
(,)
(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: 3

Show answers

Answers

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 interval is entirely above 0.5, the interval is consistent with 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 $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

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 $n = 1664, \pi = \frac{939}{1664} = 0.5643$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so Z = 1.96 .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5643 - 1.96\sqrt{\frac{0.5643*0.4357}{1644}} = 0.54$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5643 + 1.96\sqrt{\frac{0.5643*0.4357}{1644}} = 0.588$

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 interval is consistent with the statement that a majority of adult Americans would give themselves a grade of A or B.

Answer from: Quest

step-by-step explanation:

Answer from: Quest

The probability of picking 2 green markers is 2/10

Another question on Mathematics

Mathematics, 22.06.2019 02:00

Which of the following is not a solution to the inequality graphed below? (-2, -4)(-1, -5)(0, -3)(2, -1)which of the following is a solution to the inequality graphed below? select all that apply.(-3, -3)(-1, -1)(-3, -1)(2, 2)

Answers: 1

Answer

Mathematics, 22.06.2019 02:30

Factor this polynomial completely. 12x^2+ x-6

Answers: 1

Answer

Mathematics, 22.06.2019 04:20

Avegetable farmer fills of a wooden crate with of a pound of tomatoes. how many pounds of tomatoes can fit into one crate? a. 14/15 of a pound b. 2 1/10 pounds c. 1 1/14 pounds d. 10/21 of a pound

Answers: 1

Answer

Mathematics, 22.06.2019 04:30

Given: pb tangent pv,pu secants if m = 80° and m = 30°, then m 3 = 55 40 25

Answers: 1

Answer

You know the right answer?

A report on consumer financial literacy summarized data from a representative sample of 1,664 adult...

Questions