ou may need to use the appropriate appendix table or technology to answer this 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: Ha: (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.) (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 zero, so we can be 95% confident that the population proportion of adults saying that their financial security is more than fair ___.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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You may need to use the appropriate appendix table or technology to answer this 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.)

(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 ____ zero, so we can be 95% confident that the population proportion of adults saying that their financial security is more than fair _______.

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