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Text book; The Basic Practice of Statistics. 7th Edition by David Moore. William I. Micheal A. Fligner

ISBN; -13;978-1-4641-4253-6

Testing glass. How well materials conduct heat matters when designing houses. As a test of a new measurement process, 10 measurements are made on pieces of glass known to have conductivity 1. The average of the 10 measurements is 1.07. For each of the boldface numbers, indicate whether it is a parameter or a statistic. Explain your answer.

15.27Roulette. A roulette wheel has 38 slots, of which 18 are black, 18 are red, and 2 are green. When the wheel is spun, the ball is equally likely to come to rest in any of the slots. One of the simplest wagers chooses red or black. A bet of $1 on red returns $2 if the ball lands in a red slot. Otherwise, the player loses his dollar. When gamblers bet on red or black, the two green slots belong to the house. Because the probability of winning $2 is 18/38, the mean payoff from a $1 bet is twice 18/38, or 94.7 cents. Explain what the law of large numbers tells us about what will happen if a gambler makes very many bets on red.

15.29Glucose testing. Shelia’s doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. In a test to screen for gestational diabetes, a patient is classified as needing further testing for gestational diabetes if the glucose level is above 130 milligrams per deciliter (mg/dL) one hour after having a sugary drink. Shelia’s measured glucose level one hour after the sugary drink varies according to the Normal distribution with μ = 122 mg/dL and σ = 12 mg/dL.

(a)If a single glucose measurement is made, what is the probability that Shelia is diagnosed as needing further testing for gestational diabetes?

(b)If measurements are made on four separate days and the mean result is compared with the criterion 130 mg/dL, what is the probability that Shelia is diagnosed as needing further testing for gestational diabetes?

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15.33Runners. In a study of exercise, a large group of male runners walk on a treadmill for six minutes. After this exercise, their heart rates vary with mean 8.8 beats per five seconds and standard deviation 1.0 beats per five seconds. This distribution takes only whole-number values, so it is certainly not Normal.

(a)Let be the mean number of beats per five seconds after measuring heart rate for 24 five-second intervals (two minutes). What is the approximate distribution of according to the central limit theorem?

(b)What is the approximate probability that is less than 8?

(c)What is the approximate probability that the heart rate of a runner is less than 100 beats per minute? (Hint: Restate this event in terms of .)

15.35Returns on stocks . Andrew plans to retire in 40 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on past returns. He learns that from 1964 to 2013, the annual returns on U.S. common stocks had mean 13.3% and standard deviation 17.0%.6 The distribution of annual

15.37

returns on common stocks is roughly symmetric, so the mean return over even a moderate number of years is close to Normal. What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 40 years will exceed 10%? What is the probability that the mean return will be less than 5%? Follow the four-step process as illustrated in Example 15.8.

16.19Student study times. A class survey in a large class for first-year college students asked, “About how many hours do you study during a typical week?” The meanresponse of the 463 students was = 15.3 hours.5 Suppose that we know that the study time follows a Normal distribution with standard deviation σ = 8.5 hours in the population of all first-year students at this university.

(a)Use the survey result to give a 99% confidence interval for the mean study time of all first-year students.

(b)What condition not yet mentioned must be met for your confidence interval to be valid?

16.21An outlier strikes. There were actually 464 responses to the class survey in Exercise 16.19. One student claimed to study 10,000 hours per week (10,000 is more than the number of hours in a year). We know he’s joking, so we left out this value. If we did a calculation without looking at the data, we would get = 36.8 hours for all 464 students. Now what is the 99% confidence interval for the population mean? (Continue to use σ = 8.5.) Compare the new interval with that in Exercise 16.19. The message is clear: always look at your data, because outliers can greatly change your result.

16.23Explaining confidence. You ask another student to explain the confidence interval for mean ideal weight described in Exercise 16.22. The student answers, “We can be 95% confident that future samples of adult American women will say that their mean ideal weight is between 137.6 and 140.4 pounds.” Is this explanation correct? Explain your answer.

17.31I want more muscle. If young men thought that their own level of muscle was about what women prefer, the mean “muscle gap” in the study described in Exercise 16.20(page 387) would be 0. We suspect (before seeing the data) that young men think women prefer more muscle than they themselves have.

(a)State null and alternative hypotheses for testing this suspicion.

(b)What is the value of the test statistic z?

(c)You can tell just from the value of z that the evidence in favor of the alterna

17.39The wrong P. The report of a study of seat belt use by drivers says, “Hispanic drivers were not statistically significantly more likely than White/non-Hispanic drivers to overreport safety belt use (27.4 vs. 21.1%, respectively; z = 1.33, P > 1.0).”10 How do you know that the P-value given is incorrect? What is the correct one-sided P-value for test statistic z = 1.33?

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