Marvel Studio’s motion picture Guardians of the Galaxy opened over the first two daysof the 2014 Labor Day weekend to a record-breaking $94.3 million in ticket sales revenuein North America (the hollywood reporter, August 3, 2014). The ticket sales revenue indollars for a sample of 30 theaters is as follows.a. What is the 95% confidence interval estimate for the mean ticket sales revenue pertheater? Interpret this result.b. Using the movie ticket price of $8.11 per ticket, what is the estimate of the meannumber of customers per theater?c. The movie was shown in 4080 theaters. Estimate the total number of customers whosaw Guardians of the Galaxy and the total box office ticket sales for the weekend

2. According to the website Rotten Tomatoes, 94% of people who watched the Netflix show Stranger Things liked it. Since UR students tend to be scientifically minded, we hypothesize that less than 94% of UR students like the show. Out of 219 surveyed UR students, 198 indicated they like Stranger Things. Use the built in prop.test() function to: a. Construct a 90% confidence interval for the proportion of UR students who like Stranger Things. b. Test at the a=0.10 significance level whether the proportion of students who like Stranger Things is LESS THAN 0.94. What conclusion do you reach?

15. Pain after surgery: In a random sample of 50 patients undergoing a standard surgical procedure, 15 required medication for postoperative pain. In a random sample of 90 patients undergoing a new procedure, only 16 required pain medication. a. Construct a 95% confidence interval for the difference in the proportions of patients needing pain medication between the old and new procedures. b. A physician claims that the proportion of patients who need pain medication is the same for both procedures. Does the confidence interval contradict this claim? 16

3. In a survey of 2241 adults in a recent year, 650 say they made a New Year's resolution to eat healthier. Construct, by hand, a 95% confidence interval estimate of the proportion of all adults who made a New Year's resolution to eat healthier. b. Interpret your confidence interval in context of the problem. a.

In 2003, the Accreditation Council for Graduate Medical Education (ACGME) implemented new rules limiting work hours for all residents. A key component of these rules is that residents should work no more than 80 hours per week. The following is the number of weekly hours worked in 2017 by a sample of residents at the Tidelands Medical Center.                           87 89 81 81 85 76 85 85 79 81 78 79   a. What is the point estimate of the population mean? b. Develop a 90% confidence interval for the population mean. c. Is the council's claim that the "typical resident" works 80 per month reasonable?

In a study designed to determine whether there was a cluster of brain cancer cases at a Pratt & Whitney plant, record from 223,000 employees were studied and 723 employees with brain tumors were found. Treat those employees as a random sample and construct a 95% confidence interval estimate of the proportion of all adults who develop such tumors. write a brief statement interpreting that confidence interval.

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State the conclusion based on the results of the test. According to the Federal Housing Finance Board, the mean price of a single-family home two years ago was $299,100. A real estate broker believes that because of the recent credit crunch, the mean price has increased since then. The null hypothesis is not rejected. Choose the correct answer below. O A. There is not sufficient evidence to conclude that the mean price of a single-family home has increased from its level two years ago of $299,100. O B. There is sufficient evidence to conclude that the mean price of a single-family home has decreased from its level two years ago of $299,100. C. There is sufficient evidence to conclude that the mean price of a single-family home has increased from its level two years ago of $299,100. O D. There is not sufficient evidence to conclude that the mean price of a single-family home has decreased from its level two years ago of $299,100.

The following is the number of hours of sleep obtained by eight college freshmen.  Use the data to find a 92% confidence interval for the true mean number of hours of sleep by college freshmen. ​​7.5​    8.0​   6.5​  24​  8.5​  6.5​  7.0​   7.5