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4. [-/24 Points] DETAILS ASWSBE14 10.E.020.MI. MY NOTES ASK YOUR TEACHER You may need to use the appropriate appendix table or technology to answer this question. Recall the method used to obtain a confidence interval for the difference between two population means for matched samples. (a) The following data are from matched samples taken from two populations. Compute the difference value for each element. (Use Population 1 - Population 2.) Population Element 2 Difference 1 2 7 6 3 9 4 12 5 5 13 6 15 13 15 12 (b) Compute d. (c) Compute the standard deviation s. (Round your answer to two decimal places.) (d) What is the point estimate of the difference between the two population means? (Use Population 1 - Population 2.) (e) Provide a 95% confidence interval for the difference between the two population means. (Use Population 1 - Population 2. Round your answers to two decimal places.) to6. [-/20 Points] DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 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 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 for the two years. (Let p, = population proportion most recently saying financial security more than fair and p2 = population proportion from the year before saying financial security more than fair. Once the cursor is in the box the mathPad will appear to the right. Use the mathPad "Functions" option to create subscripts. Enter != for # as needed.) Ho 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 P, - P2. Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value =| State your conclusion. O Do not reject Ho. 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. O Reject Ho. 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 Ho. 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. O Reject Ho. 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) 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 ---Select--. v zero, so we can be 95% confident that the population proportion of adults saying that their financial security is more than fair [ ---Select
