Question

In: Statistics and Probability

A certain financial services company uses surveys of adults age 18 and older to determine if...

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

p1p2.

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 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.    

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 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 has increased may have stayed the same .

Solutions

Expert Solution


Related Solutions

A certain financial services company uses surveys of adults age 18 and older to determine if...
A certain 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 700 adults showed 245 indicating that their financial security was more than fair. 1.Conduct the hypothesis test and compute the p-value. At a 0.05 level of significance, what is your...
A certain financial services company uses surveys of adults age 18 and older to determine if...
A certain 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...
A certain financial services company uses surveys of adults age 18 and older to determine if...
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 1,100 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...
A certain financial services company uses surveys of adults age 18 and older to determine if...
A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. Suppose that a recent sample of 1,000 adults showed 460 indicating that their financial security was more than fair. Suppose that just a year before, a sample of 850 adults showed 340 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...
Country Financial, a financial services company, uses surveys of adults age 18 and older to determine...
Country Financial, a financial services company, uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time (USA Today, April 4, 2012). In February of 2012, a sample of 1000 adults showed 410 indicating that their financial security was more than fair. In February of 2010, a sample of  900 adults showed 315 indicating that their financial security was more than fair. What is a 95% confidence interval estimate of the difference between the...
Country Financial, a financial services company, uses surveys of adults age 18 and older to determine...
Country Financial, a financial services company, uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time (USA Today, April 4, 2012). In February of 2012, a sample of 1000 adults showed 410 indicating that their financial security was more than fair. In February of 2010, a sample of  900 adults showed 315 indicating that their financial security was more than fair. What is the point estimate of the difference between the proportions at...
Country Financial, a financial services company, uses surveys of adults age 18 and older to determine...
Country Financial, a financial services company, uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time (USA Today, April 4, 2012). In February of 2012, a sample of 1000 adults showed 410 indicating that their financial security was more than fair. In February of 2010, a sample of 900 adults showed 315 indicating that their financial security was more than fair. At 99% confidence, what is the margin of error? Round to...
In a recent survey​ conducted, a random sample of adults 18 years of age or older...
In a recent survey​ conducted, a random sample of adults 18 years of age or older living in a certain country were asked their reaction to the word socialism. In​ addition, the individuals were asked to disclose which political party they most associate with. Results of the survey are given in the table. Complete parts ​(a) through ​(c) below. _ Democrats Independents Republicans Positive 216 64 158 Negative 270 370 411 (a) Does the evidence suggest individuals within each political...
a survey of 2284 adults in a certain large country aged 18 and older conducted by...
a survey of 2284 adults in a certain large country aged 18 and older conducted by reputable polling organization founded that 424 have donated blood in the past two years. Complete Parts (a) through (C). a) obtain a point estimate for the population proportion of adults in the country age 18 and older who have donated blood in the past two years. b) verify that the requirements for constructing a confidence interval. the sample [ a) can be assumed to...
In a recent Gallup poll, 507 adults age 18 and older were surveyed and 269 said...
In a recent Gallup poll, 507 adults age 18 and older were surveyed and 269 said they believed they would not have enough money to live comfortably in retirement. Use a 0.01 significance level to test the claim that the proportion of adults who do not believe they will have enough money to live comfortably in retirement is smaller than 60%. The test statistic is:                             [ Select ]             ...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT