Question

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 800 adults showed 280 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 p₁ = population proportion most recently saying financial security more than fair and p₂ = population proportion from the year before saying financial security more than fair. Enter != for ≠ as needed.)

H₀:

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

p₁ − p₂.

Round your answer to two decimal places.)

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

p-value =

State your conclusion.

Do not reject H₀. 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.

Reject H₀. 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.    

Reject H₀. 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.

Do not reject H₀. 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 has increased may have stayed the same .

Answer 1