Which of the following conditions are necessary to construct a confidence interval for the difference in population means? (Select all that apply.) Two independent random samples from their respective populations. The parameter of interest is the difference in means for both populations. Both sample sizes must be greater than or equal to 30. The means come from normally distributed populations. Large enough sample sizes to assume the approximate normality of the sampling distributions of )71 and )72 or verification that the populations are normal. Population standard deviations for both samples are known. Many employers are concerned about employees wasting time by surfing the Internet and e-mailing friends during work hours. The article "Who Goofs Off 2 Hours a Day? Most Workers, Survey Says" summarized data from a large sample of workers. Suppose that the CEO of a national marketing firm wants to determine the difference in mean wasted time during an 8-hour workday for employees of her company at two different locations. Each person in a random sample of 10 employees from Location A (population 1) is asked about daily wasted time at work (in minutes), and 10 employees from Location B (population 2) are asked the same question. Participants were guaranteed anonymity to obtain truthful responses. Suppose the resulting data are as follows. Location A 96 136 144 100 102 139 101 104 147 86 Location B 109 107 117 118 104 106 120 119 108 102 LA USE SALT (a) Calculate the point estimate for the difference in the population means. (b) Determine the margin of error for the 90% confidence interval for the difference in population means. (Use a table or technology. Round your answer to three decimal places.) (c) Find the 90% confidence interval. (Round your answers to three decimal places.)In a study of selfadhesive bandages, a doctor wanted to see if there was truly a difference in the healing time between the self-adhesive bandages preloaded with antibiotic and the self-adhesive bandages used with an antibiotic applied to the wound. The doctor randomly selected 100 patients to participate in the study and divided them into two groups of SOGroup 1 using the bandages preloaded with antibiotic and Group 2 using the bandages with the same amount of antibiotic applied to the wound rst. In both groups, the amount of time, in days, it took for the wound to heal was recorded. In Group 1, the mean healing time was 1.39 days with a standard deviation of 0.68, and the mean for Group 2 was 2.34 days with a standard deviation of 0.76. IA uses (a) which of the following is the best way to describe this study? Experiment with 1 treatment: the types of bandages used 0 Experiment with 2 treatments: the bandages with antibiotic and the bandages with antibiotic applied first Experiment with 1 treatment: the type of antibiotic used Observational study (b) Calculate the critical value we would use for a 99% confidence interval for difference in the population means? (Use a table or technology. Round your answer to three decimal places.) (c) Find the 99% condence interval for the difference in true mean healing time in wounds between the bandages with preloaded antibiotic and the bandages with antibiotic applied to the wound rst. (Round your answers to two decimal places.) We can be 99% confident that the difference in true mean healing time in wounds for the bandages with preloaded antibiotic and the bandages with antibiotic applied to the wound first is between ( , ). (d) Determine whether the following statement is true or false. If zero lies in the interval, then there is sufcient evidence of a significant difference between the mean healing times for the 2 different bandages. True 0 False / In a study using data from the Danish Twin Registry, it is claimed that twins (specically male twins) live longer than singletons. You decide to run a test to see if this is true in the United States. You randomly sample the death records in New York City of 70 males who were born with a twin and 100 males who were born as a single birth. (a) If the mean life expectancy for all 170 males was 78.3 years with a population standard deviation of a = 4.5 years, calculate a 95% condence interval for the mean life expectancy (in years) of all males. (Use a table or technology. Round your answers to two decimal places.) ( , )y. (b) What would be the appropriate null and alternative hypotheses? (c) If after conducting the test you found a t score of 1.54 and a P-value of 0.064, what would be the appropriate conclusion if you were using a significance level of 0.05? Because 0.064 > a, we reject the null hypothesis. Because the 0.064 a, we fail to reject the null hypothesis. Because the 0.064