Answered: (a)State the hypotheses that can be…

Name: A certain financial services company uses surveys of adults age 18 and
Uploaded: 2024-03-20T07:07:00.000Z
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Description: 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. Sup

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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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 1,200 adults showed 420 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.

(A) 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.

(B) 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) 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.

(D) 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.

(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 {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 {has decreased, may have stayed the same, has increased}

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