The Music Business Association conducted a study to find out what proportion of teens and adults prefer to listen to music through ondemand streaming services such as YouTube, Pandora and Spotify. You will construct a confidence interval for a difference of two population proportions to nd the true difference in proportion of teens and adults who prefer to listen to music through on- demand streaming services. (Use a table or technology. Round your answers to two decimal places.) m USE SALT (3) Find the 2 critical value associated with 99% confidence. 2* = 2.58 \\/ (b) Find the 2 critical value associated with 95% confidence. 2* = 1.75 x You may nd the critical value by using a standard normal table or by using technology. (c) Find the 2 critical value associated with 80% confidence. * z = 1.28 J In a certain poll of 1,600 random adults the week of August 17, 2016, 67% said they thought America was "on the wrong track." A week earlier in a different random sample of 1,500 adults, 63% said they thought America was "on the wrong track." (Letf)1 be the proportion of adults from the week of August 17, 2016 who thought America was "on the wrong track" and 1'22 be the proportion of adults from the previous week who thought America was "on the wrong track.") IA use SA (a) 5 this an example of an experiment or an observational study? experiment 0 observational study J (b) For this study, the sampling distribution of the difference in sample proportions takes on an approximately normal shape. How do we know this? The sample sizes are both at least 30. We do not know this. 0 The number of success and failures in each sample are both at least 10. The samples are independent random samples. (c) Calculate a 90% condence interval for the true difference in population proportions of adults who think America is "on the wrong track." (Use a table or technology. Round your answers to three decimal places.) ( 0.504 x If 1(1 'P1) + 172(1 'P2) "1 \"2 (131 132) :1: (2 critical value) VIM + M) \"1 "2 (131 1'12) t (2 critical value)V , 0.556 x An online poll of 6,000 residents of Washington, DC showed that 71% agreed with the statement "Employers should be required to pay men and women the same salary for the same job." An online poll of 4,800 residents of Atlanta revealed that 65% agreed with the same statement. IA uses (a) Because these were online polls, what type of bias might be present? undercoverage o voluntary response bias nonresponse bias none, if the polls were anonymous J (b) How many successes were there in the Washington sample? 48 x \"1131 2 10, n1(1 f21)2 10, \"2132 2 10, n2(1 f92) 2 10 How many failures were there in the Washington sample? 16 x [11131 2 1o, n1(1 f;1)z 1o, nzz 2 1o, n2(1 1'22) 2 10 (c) Calculate a 95% condence interval for the true difference in population proportions between the people of Washington, DC, and the people of Atlanta who agree with the statement (DC Atlanta). (Use a table or technology. Round your answers to three decimal places.) ( 0.032 x A confidence interval is of the form point estimate :l: margin of error. , 0,068 x A confidence interval is of the form point estimate :t margin of error. ) According to a report on sleep deprivation, the proportion of California residents who reported insufcient rest or sleep during each of the preceding 30 days is 8.0%, while this proportion is 8.7% for Oregon residents. These data are based on simple random samples of 11,567 California and 4,694 Oregon residents. Calculate a 95% confidence interval for the difference between the proportions of Californians and Oregonians who are sleep deprived and interpret it in context of the data. (Use 1304 130R. Round your answers to two decimal places.) Before calculating the interval, we should check that the conditions are satised. The sample is B / random and the sample represents lesslhan a / 10% of all California and Oregon residents. Therefore whether or not one person in the sample reported insufficient rest or sleep is a / independent of another. The success-failure condition is a / met since the number of successes and failures is greater than a / 10. So, we are 95% confident that the difference between the proportions of Californians and Oregonians who are sleep deprived is between % and %. Consider the following data on sleep deprivation rates of Californians and Oregonians. The proportion of California residents who reported insufficient rest or sleep during each of the preceding 30 days is 9.0%, while this proportion is 9.6% for Oregon residents. These data are based on simple random samples of 11,556 California and 4,691 Oregon residents. (Use a significance level of 0.05. Use PCA - POR.) (a) Conduct a hypothesis test to determine if these data provide strong evidence that the rate of sleep deprivation is different for the two states. Check the relevant conditions. The sample is random and the sample represents less than 10% of all California and Oregon residents. Therefore whether or not one person in the sample reported insufficient rest or sleep is independent of another. The success-failure condition is met since the number of successes and failures is greater than 10. State the appropriate null and alternative hypotheses. O Ho: PCA = POR HA: PCA * POR O Ho: PCA # POR HA: PCA = POR O Ho: PCA S POR HA: PCA > POR O Ho: PCA S POR HA: PCA # POR O Ho: PCA > POR HA: PCA S POR Calculate the test statistic and determine the p-value. (Round your test statistic to two decimal places and your p-value to four decimal places.) p-value = Interpret the p-value in context of the hypothesis test and the data.Suppose a survey asked 821 randomly sampled registered voters in California "Do you support? Or do you oppose? Drilling for oil and natural gas off the Coast of California? Or do you not know enough to say?" Below is the distribution of responses, separated based on whether or not the respondent graduated from college. College Grad Yes No Support 153 131 Oppose 179 125 Do not know 103 130 Total 435 386 (a) What percent of college graduates in this sample do not know enough to have an opinion on drilling for oil and natural gas off the Coast of California? (Round your answer to two decimal places.) \"/0 What percent of the non-college graduates in this sample do not know enough to have an opinion on drilling for oil and natural gas off the Coast of California? (Round your answer to two decimal places.) /u (b) Conduct a hypothesis test to determine if the data provide strong evidence that the proportion of college graduates who do not have an opinion on this issue is different than that of non-college graduates. (Use a significance level of 0.05. Use college graduates non-college graduates for your test.) State the null and alternative hypothesis. (Use the subscripts 1 for college graduates and 2 for non-college graduates. Enter != for as needed.) H0: HA: Check the relevant conditions. Both samples are 9 / random and the samples represent less than a / 10% of their populations, so independence is a / satisfied. The success-failure condition is a / met since the number of successes and failures in each group is greaterthan e \\/ 10. State the test statistic. (Round your answer to two decimal places.) State the test statistic. (Round your answer to two decimal places.) State the pvalue. (Round your answer to four decimal places.) p-value = Interpret the p-value in context of the hypothesis test. O Reject H0. The data provide convincing evidence that the proportion of college graduates who do not have an opinion on this issue is different than that of non-college graduates. Reject H0' The data do not provide convincing evidence that the proportion of college graduates who do not have an opinion on this issue is different than that of non-college graduates. Fail to reject H0. The data provide convincing evidence that the proportion of college graduates who do not have an opinion on this issue is different than that of nonco|lege graduates. Fail to reject H0. The data do not provide convincing evidence that the proportion of college graduates who do not have an opinion on this issue is different than that of non-college graduates