You may need to use the appropriate appendix table or technologyto answer this question.
A certain financial services company uses surveys of adults age 18and older to determine if personal financial fitness is changingover time. A recent sample of 1,000 adults showed 410 indicatingthat their financial security was more than fair. Suppose that justa year before, a sample of 1,200 adults showed 420 indicating thattheir financial security was more than fair.
(a)
State the hypotheses that can be used to test for a significantdifference between the population proportions for the two years.(Let p1 = population proportion most recently saying financialsecurity more than fair and p2 = population proportion from theyear before saying financial security more than fair. Enter != for? as needed.)
H0:
Ha:
(b)
Conduct the hypothesis test and compute the p-value. At a 0.05level 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 =
Incorrect:
State your conclusion.
Do not reject H0. There is insufficient evidence to conclude thepopulation proportions are not equal. The data do not suggest thatthere has been a change in the population proportion saying thattheir financial security is more than fair.
Do not reject H0. There is sufficient evidence to conclude thepopulation proportions are not equal. The data suggest that therehas been a change in the population proportion saying that theirfinancial security is more than fair.
Reject H0. There is insufficient evidence to conclude thepopulation proportions are not equal. The data do not suggest thatthere has been a change in the population proportion saying thattheir financial security is more than fair.
Reject H0. There is sufficient evidence to conclude the populationproportions are not equal. The data suggest that there has been achange in the population proportion saying that their financialsecurity is more than fair.
Correct: Your answer is correct.
(c)
What is the 95% confidence interval estimate of the differencebetween the two population proportions? (Round your answers to fourdecimal places.)
_____
to
_____
What is your conclusion?
The 95% confidence interval zero, so we can be 95% confident thatthe population proportion of adults saying that their financialsecurity is more than fair .
