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 1,100 adults showed 385 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 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.

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.

(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 ---Select--- 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 ---Select--- has decreased may have stayed the same has increased .