Acertain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. suppose that in february 2012, a sample of 1,000 adults showed 410 indicating that their financial security was more than fair. in february 2010, 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 saying financial security more than fair in 2012 and p2 = population proportion saying financial security more than fair in 2010.)

h0: p1 − p2 = 0
ha: p1 − p2 ≠ 0
h0: p1 − p2 > 0
ha: p1 − p2 ≤ 0
h0: p1 − p2 ≠ 0
ha: p1 − p2 = 0
h0: p1 − p2 ≥ 0
ha: p1 − p2 < 0
h0: p1 − p2 ≤ 0
ha: p1 − p2 > 0

(b) what is the sample proportion indicating that their financial security was more than fair in 2012?
what is the sample proportion indicating that their financial security was more than fair in 2010?

(c) 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. (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 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 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 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.

(d) what is the 95% confidence interval estimate of the difference between the two population proportions? (round your answers to four decimal places.)