Statistical Lab Background A majority of smokers in the United States (56%) believe they are at least occasionally discriminated against in public life or employment because of their smoking. In comparison, just 17% Americans who are overweight feel they have been discriminated against at some point because of their weight. Guidelines In this lab, you will do the following. . Estimate the difference between two population proportions with a 95% confidence interval. . Verify the conditions for computing a confidence interval. . Interpret the confidence interval. About the Data The data were collected by Gallup in 2013 and 2017.Are insurance companies justied in charging higher insurance premiums to individuals who smoke? What about charging higher insurance premiums for individuals who are signicantly overweight? In 2013, Gallup asked a random sample of 2,027 American adults these questions. Later, in 2017, Gallup asked a random sample of 1,021 American adults these same questions. In 2013, 58% of respondents reported that insurance companies were justied in charging higher premiums to smokers. How many individuals from the 2013 survey reported higher premiums were justied for smokers? (Round your answer to the nearest whole number.) In 2017, 59% of respondents reported that insurance companies were justied in charging higher premiums to smokers. How many individuals from the 2017 survey reported higher premiums were justied for smokers? (Round your answer to the nearest whole number.) Is there a statistically measurable change in the proportion of Americans who believe that insurance companies are justied in charging higher premiums for smokers? Define group 1 to be 2017 and group 2 to be 2013. Compute a 95% condence interval to estimate the difference in opinions for these 2 years alter verifying the conditions. (a) The large-sample condition is easily verified with some simple math. If I113 is at least 10 and is also at least 10 for both samples, then this condition is satised. In other words, if there are at least ten successes and ten failures in both samples, then the condition is satised. For the 2013 sample, compute and report the following. (Round your answers to the nearest whole number.) \"2P2 = n20 1'22) = For the 2017 sample, compute and report the following. (Round your answers to the nearest whole number.) \"1P1 = n10 131) = Are these quantities at least 10 for both samples? 0 Yes ONo (b) The condition that both samples are independent random samples or that both samples are representative of the corresponding populations is checked next. Did Gallup collect both samples randomly and independently from the population of American adults? O No, Gallup is a business that is concerned only with making money. 0 No, Gallup cannot use random methods in the selection of its samples. O Yes, Gallup stated that it used random sampling methods to collect these data. 0 Yes, Gallup used the same exact sample in 2017 as it did in 2013. (c) What is the estimated difference in proportion of Americans who report that insurance companies are justied in charging higher insurance premiums for smokers? (131 132) For a 95% condence interval estimate of the difference, what is the appropriate 2 critical value? (Round your answer to two decimal places.) What is the margin of error for this condence interval? (Round your answer to three decimal places.) What is the lower limit for the confidence interval? (Round your answer to three decimal places.) What is the upper limit for the condence interval? (Round your answer to three decimal places.) (d) Communicate the results by interpreting the condence interval. 0 We are 95% condent that more Americans are in favor of higher insurance premiums for smokers today and that the difference in the proportion among Americans in 2017 versus 2013 is between -2.7% and 4.7%. 0 Because 0 is included in the condence interval, is it plausible that the proportion of American adults in favor of higher premiums for smokers in 2017 is different from the proportion in 2013, with there being more in favor in 2017. 0 Because 0 is included in the condence interval, it is plausible that the proportion of American adults in favor of higher premiums for smokers in 2017 is not different from the proportion in 2013. 0 We are 95% condent that fewer Americans are in favor of higher insurance premiums for smokers today and that the difference in the proportion among Americans in 2017 versus 2013 is between 2.7% and 4.7%. (e) You can verify these results by conducting a hypothesis test for the difference between two population proportions on these data. Define your level of significance at a = (100 - 95)%. Your test conclusion should match the interpretation for the 95% confidence interval if ---Select--- Let us investigate the other proportion. In 2013, 41% of respondents reported that insurance companies were justified in charging higher premiums to individuals who are significantly overweight. How many individuals from the 2013 survey reported higher premiums were justified for the significantly overweight? (Round your answer to the nearest whole number.) In 2017, 37% of respondents reported that insurance companies were justified in charging higher premiums to individuals who are significantly overweight. How many individuals from the 2017 survey reported higher premiums were justified for the significantly overweight? (Round your answer to the nearest whole number.) Is there a statistically measurable change in the proportion of Americans who believe that insurance companies are justified in charging higher premiums for individuals who are significantly overweight? Define group 1 to be 2017 and group 2 to be 2013. Perform a hypothesis test to determine the answer. Let the significance level be defined at a = 0.05. (a) Write the hypothesis statement. Ho: P1 - P2 = Ha: P1 - P2 ? vo ( b ) The large-sample condition is easily verified with some simple math. If np is at least 10 and n(1 - p) is also at least 10 for both samples, then this condition is satisfied. In other words, if there are at least ten successes and ten failures in both samples, then the condition is satisfied. For the 2013 sample, compute and report the following. (Round your answer to the nearest whole number.) n2P2 = 72(1 - P2) = For the 2017 sample, compute and report the following. (Round your answer to the nearest whole number.) njP1 = n1(1 - p1) = Are these quantities at least 10 for both samples? Yes O No (c) The condition that both samples are independent random samples or that both samples are representative of the corresponding populations has already been checked in part (b) above. (a) Compute and report the combined estimate of the common population proportion, p. = _1 1 21 2. (Round your answer to three decimal places.) n1 + 02 Pc =(e) Using your rounded answer for 13': above, compute (by hand) and report the test statistic z = . (Round your answer to two decimal places.) (f) Find the P-value for your 2 in a statistical table and report the two-sided P-value. (Round your answer to three decimal places.) p: (9) What is the decision for this test? 0 Reject the null hypothesis because the P-value is less than a. O Fail to reject the null hypothesis because the Pvalue is less than a. O Fail to reject the null hypothesis because the P-value is greater than a. O Reject the null hypothesis because the P-value is greater than a. (h) What is the conclusion for this test? Write one or two sentences to communicate the results from this hypothesis test