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Suppose a company wants to estimate the true mean call duration for their telephone service representatives. In a sample of 2000 calls, the sample mean duration was 143.0 seconds, with an associated 95% confidence interval of 141.7 to 144.3 seconds. Suppose the assumptions of the procedure they used were met. Of the following options, which one is the best interpretation of that interval? O We can be 95% confident that the sample mean call duration of the 2000 calls lies between 141.7 and 144.3 seconds. ) In repeated sampling, 95% of the 95% confidence intervals calculated in this manner will capture the sample mean call duration. We can be 95% confident that the true mean call duration for telephone service representatives in this company lies between 141.7 and 144.3 seconds. We can be 95% confident that the sample mean call duration for telephone service representatives in all companies lies between 141.7 and 144.3 seconds.Suppose researchers are investigating the effectiveness of two different COVID-19 vaccines. As part of a large-scale study, forty thousand volunteers are randomly assigned to one of two groups. One group received a vaccine made by Fizzier, the other group a vaccine made by Modia. They intend to follow up the volunteers for 3 months, then see if there is a difference in the proportions of individuals who contract COVID-19. Of the following options, which one is the most appropriate set of hypotheses for the most appropriate hypothesis test? HO : OF = OM, Ha : OF # OM OHo : PF = PM, Ha : PF # PM OHo : PF = PM, Ha : PF + PM Ho : PF + PM. Ha : PF = PMWhich of the following statements about hypothesis tests on a single mean are true? There may be more than one correct statement; check all that are true. Assume that all assumptions of the test are perfectly justified, and that all testing is carried out with a two-sided alternative hypothesis. a) All else being equal, the greater the sample size, the greater the power of the test. () b) The probability of a Type | error and the probability of a Type II error are always equal. c) If the true value of mu is equal to the hypothesized value of mu, we cannot make a Type II error. d) The significance level of a test is always chosen to be 0.5, since there are two equally likely outcomes