A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. A recent sample of 1,000 adults showed 410 indicating...

A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. A recent sample of 1,000 adults showed 410 indicating that their financial security was more than fair. Suppose that just a year before, a sample of 1,200 adults showed 420 indicating that their financial security was more than fair.

(a)State the hypotheses that can be used to test for a significant difference between the population proportions for the two years. (Let
p
₁
= population proportion most recently saying financial security more than fair and
p
₂
= population proportion from the year before saying financial security more than fair. Enter != for ≠ as needed.)

H
₀:

H
_a:

(b)
Conduct the hypothesis test and compute the
p
-value. At a 0.05 level of significance, what is your conclusion?

Find the value of the test statistic. (Use
p
₁
− p
₂
.

Round your answer to two decimal places.)

Find thep-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

(A) Do not reject
H
₀. There is sufficient evidence to conclude the population proportions are not equal. The data suggest that there has been a change in the population proportion saying that their financial security is more than fair.

(B) Reject
H
₀. There is sufficient evidence to conclude the population proportions are not equal. The data suggest that there has been a change in the population proportion saying that their financial security is more than fair.

(C) Do not reject
H
₀. There is insufficient evidence to conclude the population proportions are not equal. The data do not suggest that there has been a change in the population proportion saying that their financial security is more than fair.

(D) Reject
H
₀. There is insufficient evidence to conclude the population proportions are not equal. The data do not suggest that there has been a change in the population proportion saying that their financial security is more than fair.

(c)
What is the 95% confidence interval estimate of the difference between the two population proportions? (Round your answers to four decimal places.)

____to ____

What is your conclusion?

The 95% confidence interval {contains ,is completely above, is completely below zero}, so we can be 95% confident that the population proportion of adults saying that their financial security is more than fair {has decreased, may have stayed the same, has increased}

Jun 07, 2022

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A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. A recent sample of 1,000 adults showed 410 indicating...

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