Country Financial, a financial services company, uses surveys of adults age 18 and older to determine whether personal financial fitness is changing over time. A recent sample of 1000 adults showed 410 indicating that their financial security was more than fair. Just a year prior, a sample of 900 adults showed 315 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. Ho : P1 - p2 - Select your answer - H: P1 - P2 Select your answer - b. Conduct the hypothesis test and compute the p-value. Round your answer to four decimal places. p-value D At a = 0.05 level of significance, what is your conclusion? I. Reject Ho. There is not sufficient evidence to conclude that 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. II. Reject Ho. There is sufficient evidence to conclude that 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. III. Do not reject Ho. There is not sufficient evidence to conclude that 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. IV. Do not reject Ho. There is sufficient evidence to conclude that 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. Select your answer - c. What is the 95% confidence interval estimate of the difference between the two population proportions? Round your answers to four decimal places. 95% Confidence Interval ( to
Country Financial, a financial services company, uses surveys of adults age 18 and older to determine whether personal financial fitness is changing over time. A recent sample of 1000 adults showed 410 indicating that their financial security was more than fair. Just a year prior, a sample of 900 adults showed 315 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. Ho : P1 - p2 - Select your answer - H: P1 - P2 Select your answer - b. Conduct the hypothesis test and compute the p-value. Round your answer to four decimal places. p-value D At a = 0.05 level of significance, what is your conclusion? I. Reject Ho. There is not sufficient evidence to conclude that 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. II. Reject Ho. There is sufficient evidence to conclude that 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. III. Do not reject Ho. There is not sufficient evidence to conclude that 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. IV. Do not reject Ho. There is sufficient evidence to conclude that 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. Select your answer - c. What is the 95% confidence interval estimate of the difference between the two population proportions? Round your answers to four decimal places. 95% Confidence Interval ( to
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Country Financial**, a financial services company, uses surveys of adults age 18 and older to determine whether personal financial fitness is changing over time. A recent sample of 1000 adults showed 410 indicating that their financial security was more than fair. Just a year prior, a sample of 900 adults showed 315 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.**
\( H_0 : p_1 - p_2 = \) [Select your answer]
\( H_a : p_1 - p_2 \neq \) [Select your answer]
b. **Conduct the hypothesis test and compute the \( p \)-value. Round your answer to four decimal places.**
\( p \)-value = [ ]
At \( \alpha = 0.05 \) level of significance, what is your conclusion?
I. Reject \( H_0 \). There is not sufficient evidence to conclude that 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.
II. Reject \( H_0 \). There is sufficient evidence to conclude that 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.
III. Do not reject \( H_0 \). There is not sufficient evidence to conclude that 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.
IV. Do not reject \( H_0 \). There is sufficient evidence to conclude that 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.
- [Select your answer]
c. **What is the 95% confidence interval estimate of the difference between the two population proportions? Round your answers to four decimal places.**
95% Confidence Interval ( [ ] to [ ] )](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6387f1fe-f7de-460c-a439-51c8967659dd%2F9f426846-b5cf-44da-85be-ebc7e4bbd96f%2Fiku3v9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Country Financial**, a financial services company, uses surveys of adults age 18 and older to determine whether personal financial fitness is changing over time. A recent sample of 1000 adults showed 410 indicating that their financial security was more than fair. Just a year prior, a sample of 900 adults showed 315 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.**
\( H_0 : p_1 - p_2 = \) [Select your answer]
\( H_a : p_1 - p_2 \neq \) [Select your answer]
b. **Conduct the hypothesis test and compute the \( p \)-value. Round your answer to four decimal places.**
\( p \)-value = [ ]
At \( \alpha = 0.05 \) level of significance, what is your conclusion?
I. Reject \( H_0 \). There is not sufficient evidence to conclude that 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.
II. Reject \( H_0 \). There is sufficient evidence to conclude that 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.
III. Do not reject \( H_0 \). There is not sufficient evidence to conclude that 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.
IV. Do not reject \( H_0 \). There is sufficient evidence to conclude that 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.
- [Select your answer]
c. **What is the 95% confidence interval estimate of the difference between the two population proportions? Round your answers to four decimal places.**
95% Confidence Interval ( [ ] to [ ] )
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