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1. Determine whether the data described are continuous, discrete, nominal or ordinal: a) (2 points) Brands of cars sold in a dealership on weekends. b) (2 points) Temperature of a rock on equatorial Mars. c) (2 points) Ranks in U.S Army. d) (2 points) Number of calculators sold by Texas Instruments in 2020. 2. Specify the type of bias involved for the following: a) (2 points) A university conducted a survey in which faculty interviewed students to ask about the percentage of times that they wash their hands after using the bathroom. Faculty reported that 98% of the students interviewed said that they wash their hands every time they use the bathroom. b) (2 points) A student gets a good grade on a test and tells herself that she studied hard or is good at the material. She gets a bad grade on another test and says the teacher does not like her or the test was unfair. c) (2 points) An international company surveys a sample of 1000 managers and polls them about their workload. Out of 78 completed surveys, 72 of them stated that their workload is below their expectation.3. The following data represents the annual costs in dollars, of a sample of 22 popular magazine subscriptions: 14.98 9.97 20.99 7.97 9.99 11.97 116.99 14.95 11.97 16.00 9.97 17.98 38.95 14.98 14.98 16.00 24.99 14.98 10.99 18.00 12.99 11.99 a) (2 points) Find the mean annual subscription cost. b) (2 points) Find the median annual subscription cost. c) (2 points) What is the mode? 4. In a statistics class of 50 students, there were 22 men and 28 women. Nine of the men and thirteen of the women received an A in the course. A student is chosen at random from the class. a) (1 points) Find the probability that the student did not receive an A. b) (2 points) Find the probability that the student is a man or received an A. c) (2 points) Find the probability that the student did not receive an A, given that the student is a woman. 5. The Student Council at a certain school has 13 members. Four members will form an executive committee consisting of a president, a vice president, a secretary, and a treasurer. a) (3 points) In how many ways can these four positions be filled? b) (3 points) What is the probability that Sarah, Josh, Derek, and Kelly are the four committee members? 6. Five teenagers are selected at random. Let X be the number of them who have sent text messages on their cell phones within the past 30 days. According to a study by the Owngoon Company, the probability distribution of X is as follows: X 0 1 2 3 4 5 P(X) 0.015 0.097 0.258 0.343 0.227 0.060 a) (2 points) Find P(less than 2). b) (2 points) Find the probability that three or more of the teenagers sent text messages. :) (3 points) Compute the mean ux. d) (3 points) Compute the standard deviation Ox. 7. The National Health and Nutrition Survey reported that 24% of adults in the United States have hypertension. A sample of 9 adults is studied. a) (3 points) What is the probability that exactly 6 of them have hypertension? b) (3 points) What is the probability that at least 2 have hypertension? c) (2 points) Would it be unusual if more than 8 of them have hypertension? Why?8. Cherry trees in a certain orchard have heights that are normally distributed with mean of 112 inches and standard deviation of 14 inches. a) (3 points) What proportion of trees are more than 120 inches tall? b) (3 points) What proportion of trees are less than 100 inches tall? c) (3 points) What is the probability that a randomly chosen tree is between 90 and 100 inches? d) (3 points) Find the probability 30% of the shortest cherry trees were less than how many inches. 9. In a simple random sample of 144 households, the sample mean number of personal computers was 1.28. Assume the population standard deviation is 0.36. ) (6 points) Construct a 95% confidence interval for the mean number of personal computers. b) (2 points) If the sample size were 121 rather than 144, would the margin of error be larger or smaller than the result in part (a)? Explain. 10. (7 points) A study by the Web metrics firm Experian showed that in August 2011, the mean time spent per visit to Facebook was 20.8 minutes. Assume the standard deviation is 6 minutes. Suppose that a simple random sample of 225 visits in August 2013 has a sample mean of 23 minutes. A social scientist is interested to know whether the mean time of Facebook visits has increased. Perform an appropriate hypothesis test with a = 0.05 level of significance. 11. (8 points) A manager of a grocery store needs to manage the number of customers in his store to maintain safe conditions during the pandemic. He takes the following measurements of the customers in the store: 120 150 110 100 80 140 130 120 Assuming that the population is approximately normal, construct a 95% confidence interval for the population mean. 12. In a survey of adults with diabetes, the average body mass index (BMI) in a sample of 122 women was 31.1 with a standard deviation of 0.2. the BMI in a sample of 94 men was 30.4, with a standard deviation of 0.6. ) (7 points) Construct a 99% confidence interval for the difference in mean BMI between women and men with diabetes. b) (2 points) Does the confidence interval contradict the claim that the mean BMI is the same for both men and women with diabetes? Explain. 13. (7 points) Blood glucose levels for obese patients have a mean of 100. A researcher thinks that a diet high in raw cornstarch will have a positive or negative effect on blood glucose levels. A sample of 25 patients who have tried the raw cornstarch diet have a mean glucose level of 140 with a standard deviation of 15. Test the hypothesis that the raw cornstarch had an effect