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 of1,000 adultsshowed 410 indicating that their financial security was more than fair. Suppose that just a year before, a sample of1,100adultsshowed385indicating 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 thetwo years.(Letp₁= populationproportion most recently saying financial security more than fair andp₂= populationproportion from the year before saying financial security more than fair. Once the cursor is in the box the mathPad will appear to the right. Use the mathPad "Functions" option to create subscripts. Enter != foras needed.)

H₀:

H_a:

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

Find the value of the test statistic. (Usep₁p₂.

Round your answer to two decimal places.)

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

p-value =

State your conclusion.

A) RejectH₀. 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.

B) Do not rejectH₀. 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) Do not rejectH₀. 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.

D) RejectH₀. 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.)