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Introduction To Probability And Statistics 15th Edition William Mendenhall Iii , Robert Beaver , Barbara Beaver - Solutions
Refer to Example 9.14. Is there evidence of a difference in the proportions favoring the proposal for the two sections of the city?1. Select Stat ➤ Basic Statistics ➤ 2 Proportions, select Summarized data in the top drop-down list, and enter the values for n1, n2, x1, and x2 in the appropriate
Use the data from Example 8.11 involving citizens opinions about a bond proposal, reproduced here.Suppose that the citizens in the developing section of the city have no opinion about this proposal, so that they are equally likely to favor as oppose the proposal. Test : =.5 0 H p against : .5 a H
The random sample of n 5 100 Americans in Example 9.7 had an average of 3400 mg of sodium per day, with a sample standard deviation of 1100 mg. Does this provide sufficient evidence to indicate that the average daily sodium intake for Americans is more than 3300?1. Select Stat ➤ Basic Statistics
17. Baby’s Sleeping Position Does a baby’s sleeping position affect the development of motor skills? A study in the Archives of Pediatric Adolescent Medicine examined 343 full-term infants at their 4-month checkups for various milestones, such as rolling over, grasping a rattle, reaching for an
16. Winter Driving A USA Today snapshot shows that men and women feel differently about driving in winter conditions, as shown in the following graphic.20 Suppose that the survey involved random samples of 398 women and 491 men who drive in snowDoes the data indicate that there is a difference in
15. HRT, continued Refer to Exercise 14. Calculate a 99% lower one-sided confidence bound for the difference in the risk of dementia for women using hormone replacement therapy versus those who do not. Would this difference be of practical importance to a woman considering HRT? Explain.
14. Hormone Therapy and Alzheimer’s Disease A 4-year experiment involving 4532 women was conducted at 39 medical centers to study the benefits and risks of hormone replacement therapy (HRT). Half of the women took placebos and half used a widely prescribed type of hormone replacement therapy.
13. M&M’S Does Mars, Inc. use the same proportion of red M&M’S in its plain and peanut varieties? Random samples of plain and peanut M&M’S provide the following sample data:a. Use a test of hypothesis to determine whether there is a significant difference in the proportions of red
12. Tai Chi and Fibromyalgia A small study indicates that tai chi, an ancient Chinese practice of exercise and meditation, may relieve symptoms of chronic painful fibromyalgia. The study assigned 66 fibromyalgia patients to take either a 12-week tai chi class ( =33) 1 n , or attend a wellness
11. Bolts Random samples of 200 bolts manufactured by a type A machine and 200 bolts manufactured by a type B machine showed 16 and 8 defective bolts, respectively. Do these data present sufficient evidence to suggest a difference in the performance of the machine types? Use a 5.05.
2. Boomers, Gen Xers, and Millennial Men Is there a difference in the time spent doing household chores among men, depending on the generation to which they belong? The information that follows is adapted from an Advertising Age study, based on random samples of 1136 men and 795 womena. Is there a
3. White-Tailed Deer A study of the habits of whitetailed deer that indicate that they live and feed within very limited ranges—approximately 150 to 205 acres.24 To determine whether there was a difference between the ranges of deer located in two different geographic areas, 40 deer were caught,
4. Adolescents and Social Stress In a study to compare ethnic differences in adolescents’ social stress, researchers recruited subjects from three middle schools in Houston, Texas.25 The students were asked how their family’s socioeconomic status compared with others(much worse off, somewhat
2. Repeat the analysis using the data from the British study in which one group took 500 mg of aspirin every day and the control group took none. Based on their data, is the British claim justified? On Wednesday, January 27, 1988, the front page of the New York Times read, “Heart attack risk
1. Test whether the American study does in fact indicate that the rate of heart attacks for physicians taking 325 mg of aspirin every other day is significantly different from the rate for those on the placebo. Is the American claim justified? On Wednesday, January 27, 1988, the front page of the
17. Increased Yield A researcher has shown that a new irrigation/fertilization regimen produces an increase of 2 bushels per quadrat (significant at the 1% level) when compared with the regimen currently in use. The cost of implementing and using the new regimen will not be a factor if the increase
16. Suppose you wish to detect a difference between m1 and m2 (either m1 . m2 or m1 , m2) and, instead of running a two-tailed test using a 5 .05, you use the following test procedure. You wait until you have collected the sample data and have calculated 1 x and 2 x . If 1 x is larger than 2 x ,
15. Breaststroke, continued Refer to Exercise 14.a. Construct a 99% confidence interval for the difference in the average number of meters swum by breaststroke versus individual medley swimmers.b. How much longer do pure breaststroke swimmers practice that stroke than individual medley swimmers?
14. Breaststroke Swimmers How much training time does it take to become a world-class breaststroke swimmer?A survey published in The American Journal of Sports Medicine reported the number of meters per week swum by two groups of swimmers—those who competed only in breaststroke and those who
13. English as a Second Language The state of California monitors the progress of students whose native language is not English using the California English Language Development Test.28 Test results for two school districts in Riverside, California for the 2016–17 school year that follow gives
12. Heights and Gender It is a well-accepted fact that males are taller on the average than females. But how much taller? The genders and heights of 105 biomedical students are summarized here.a. Perform a test of hypothesis to either confirm or refute our initial claim that males are taller on the
11. Goin’ to the Chapel? If you choose to marry, what type of wedding site will you pick? A USA Today snapshot claims that 43% of all brides-to-be choose a house of worship for their wedding site.In a follow-up study, a random sample of 100 brides-tobe found that 46 of those sampled had chosen or
10. PCBs, continued Refer to Exercise 9.a. Calculate b and 1−b if the true mean ppm of PCBs is 6 ppm.b. Calculate b and 1−b if the true mean ppm of PCBs is 7 ppm.c. Find the power, 1−b, when m 58, 9,10, and 12. Use these values to construct a power curve for the test in Exercise 9.d. For what
8. A Maze Experiment A rat is run in a T maze and the result of each run (right or left) is recorded. A reward in the form of food is always placed at the right exit, so that if learning is taking place, the rat will choose the right exit more often than the left. If no learning is taking place,
7. SAT Scores How do California high school students compare to students nationwide in their college readiness as measured by their SAT scores? The national averages for the class of 2017 were 533 on Evidence-Based Reading and Writing and 527 on the math portion.26 Suppose that 100 California
6. Actinomycin D A biologist hypothesizes that high concentrations of actinomycin D inhibit RNA synthesis in cells and hence the production of proteins as well. To test this theory, he compared the RNA synthesis in cells treated with two concentrations of actinomycin D: .6 and .7 microgram per
5. Adolescents and Social Stress, continued Refer to Exercise 4. Some thought should have been given to designing a test for which b is tolerably low when p1 exceeds p2 by an important amount. For example, find a common sample size n for a test with a 5 .05 and b # .20 when in fact p1 exceeds p2 by
10. Treatment versus Control An experiment was conducted to test the effect of a new drug on a viral infection.After the infection was induced in 100 mice, the mice were randomly split into two groups of 50. The control group received no treatment for the infection, while the other group received
8. Ride in a Driverless Car? In a Pew Research report concerning the rise of automation in the United States, 56%of the participants indicated that they would not ride in a driverless car, and 87% favor a requirement of having a human in the driver’s seat in case of an emergency.14 Suppose that
7. Why Diet? A USA Today snapshot reported the results of a random sample of 500 women who were asked what reasons they might have to consider dieting, 13 with the following results:Can we conclude that more than 60% of women considering dieting, do so to “improve their health?”a. How would you
Calculate the p-value for the hypothesis tests given in Exercises 6. The same tests were performed in Exercises 3. Do the conclusions based on a fixed rejection region agree with those found using the p-value approach? Should they? 6. Seventy-two successes in a random sample of n 120. You wish to
Calculate the p-value for the hypothesis tests given in Exercises 5. The same tests were performed in Exercises 2. Do the conclusions based on a fixed rejection region agree with those found using the p-value approach? Should they? 5. n=1400 and x = 529 successes. You wish to show that p differs
Calculate the p-value for the hypothesis tests given in Exercises 4. The same tests were performed in Exercises 1. Do the conclusions based on a fixed rejection region agree with those found using the p-value approach? Should they? 4. n=1000 and x = 279. You wish to show that p
3. Seventy-two successes were observed in a random sample of n5120 observations from a binomial population.You wish to show that p> .5. State the null and alternative hypotheses;calculate the appropriate test statistic; provide an a 5.05 rejection region; and state your conclusions.
2. A random sample of n51400 observations from a binomial population produced x5529 successes. You wish to show that p differs from .4. State the null and alternative hypotheses;calculate the appropriate test statistic; provide an a 5.05 rejection region; and state your conclusions.
1. A random sample of n51000 from a binomial population contained 279 successes. You wish to show that p
Regardless of age, about 20% of American adults participate in fitness activities at least twice a week. Does this percentage decrease as people get older? In a local survey of n5100 adults over 40 years old, a total of 15 people indicated that they participated in a fitness activity at least twice
22. Big Kids To determine whether there is a significant difference in the weights of boys and girls beginning kindergarten, random samples of 50 boys and 50 girls aged 5 years produced the following informationa. Do you have a preconceived idea of what to expect when examining the average weights
21. What’s Normal II Of the 130 people in Exercise 29(Section 9.2), 65 were female and 65 were male.4 The means and standard deviations of their temperatures(in degrees Fahrenheit) are shown here.a. Use the p-value approach to test for a significant difference in the average temperatures for
20. Noise and Stress In Exercise 17 (Section 8.4), you compared the effect of stress in the form of noise on the ability to perform a simple task. A group of 30 subjects acted as a control, while a group of 40 (the experimental group) had to perform the task while loud rock music was played. The
19. Cheaper Airfares Looking for a great airfare?Perhaps you could lower your costs by checking fares at airports that might be slightly farther from your home, but where fares are lower. For example, the average of all domestic ticket prices at Los Angeles International Airport (LAX) was quoted11
18. Electric Cars Although there is a big difference in costs between a Tesla S and a Chevrolet Bolt, is there a difference in the range of miles for these vehicles between charges? Suppose that the results of driving tests are as followsIs there sufficient evidence to indicate a difference in the
17. SAT s, again How do states stack up against each other in SAT scores? To compare California and Massachusetts scores, random samples of 100 students from each state were selected and their SAT scores recorded with the following resultsa. Use the critical value approach to test for a significant
9. New Tax Laws The new tax structure is supposed to help small businesses survive. It is known that presently 20% of all small businesses fail in their first year.15 In a random sample of n5200 new small businesses followed for one year after opening, 30 were recorded as failed.a. If we wish to
10. Plant Genetics A peony plant with red petals was crossed with another plant having streaky petals. A geneticist states that 75% of the offspring resulting from this cross will have red flowers. To test this claim, 100 seeds from this cross were collected and germinated, and 58 plants had red
11. Early Detection of Breast Cancer Of those women who are diagnosed to have early-stage breast cancer, one-third eventually die of the disease. Suppose a screening program for the early detection of breast cancer was started in order to increase the survival rate p of those diagnosed to have the
8. Suppose that, for practical reasons, you know that p1 cannot be larger than p2. Test the appropriate hypothesis using a 5.10. Independent random samples of 140 observations were randomly selected from binomial populations 1 and 2, respectively. Sample 1 had 74 successes and sample 2 had 81
7. Suppose that you have no preconceived idea as to which parameter, p1 or p2 is larger. Test the appropriate hypothesis using a 5.10. Independent random samples of 140 observations were randomly selected from binomial populations 1 and 2, respectively. Sample 1 had 74 successes and sample 2 had 81
Drawing Conclusions Using p-Values Independent random samples were selected from two binomial populations, with sample sizes and the number of successes given. State the null and alternative hypotheses to test for a difference in the two population proportions.Calculate the necessary test
Drawing Conclusions Using p-Values Independent random samples were selected from two binomial populations, with sample sizes and the number of successes given. State the null and alternative hypotheses to test for a difference in the two population proportions.Calculate the necessary test
Calculate the necessary test statistic, the rejection region with = .05, and draw the appropriate conclusions 4. You want to show that p1 is larger than p2 using the information in Exercise 2.
Calculate the necessary test statistic, the rejection region with = .05, and draw the appropriate conclusions 3. You want to show that there is a difference in the population proportions using the information in Exercise 1.
Preliminary Calculations Independent random samples were selected from two binomial populations, with sample sizes and the number of successes given. Use this information to calculateˆ1 p , ˆ2 p , and ˆp. 2. n =60, n =60, x =43, x =36
Preliminary Calculations Independent random samples were selected from two binomial populations, with sample sizes and the number of successes given. Use this information to calculateˆ1 p , ˆ2 p , and ˆp. 1. n=1250, n=1100, x=565, x=621
The records of a hospital show that 52 men in a sample of 1000 men versus 23 women in a sample of 1000 women were admitted because of heart disease. Do these data present sufficient evidence to indicate a higher rate of heart disease among men admitted to the hospital? Use a 5.05.
17. Man’s Best Friend The Humane Society reports that there are approximately 89.7 million dogs owned in the United States and that approximately 35% of all U.S. households own large dogs.17 In a random sample of 300 households, 114 households said that they owned large dogs. Does this data
16. Washing Machine Colors A manufacturer of automatic washers provides a particular model in one of three colors—white, black, and stainless steel. Of the first 1000 washers sold, it is noted that 400 were white.Can you conclude that more than one-third of all customers have a preference for
15. A Cure for Insomnia An experimenter has prepared a drug-dose level that he claims will induce sleep for at least 80% of people suffering from insomnia. After examining the dosage we feel that his claims regarding the effectiveness of his dosage are too high. In an attempt to disprove his claim,
14. Taste Testing, continued In Exercise 13, we tried to prove that the national brand tasted better than the store brand.16 Perhaps, however, the store brand has a better taste than the national brand! If this is true, then the store brand should be judged as better more than 50% of the time.a.
13. Taste Testing In a head-to-head taste test of storebrand foods versus national brands, Consumer Reports found that it was hard to find a taste difference in the two.16 If the national brand is indeed better than the store brand, it should be judged as better more than 50% of the time.a. State
12. Sweet Potato Whitefly Suppose that 10% of the fields in a given agricultural area are infested with the sweet potato whitefly. One hundred fields in this area are randomly selected, and 25 are found to be infested with whitefly.a. Assuming that the experiment satisfies the conditions of the
16. Starting Salaries, again As a group, students majoring in the engineering disciplines have the highest salary expectations, followed by those studying the computer science fields, according to a Michigan State University study.8 To compare the starting salaries of college graduates majoring in
4. If these questions were asked today, would you expect the responses to be similar to those reported here or would you expect them to differ significantly?When Americans eat out at restaurants, most choose American food; however, tastes for Mexican, Chinese, and Italian food vary from region to
3.a. Construct a 95% confidence interval for the proportion of Americans who ate together seven nights a week.b. Construct a 95% confidence interval for the difference in the proportion of women and men who personally cook at least 4+ meals per week.c. Construct a 95% confidence interval for the
2. Do the numbers in the tables indicate the number of people/families in the categories?If not, what do those numbers represent?When Americans eat out at restaurants, most choose American food; however, tastes for Mexican, Chinese, and Italian food vary from region to region of the United States.
1. Verify the margin of error of 63 percentage points as stated for the sample of n5936 adults. Suppose that the sample contained an equal number of men and women or 468 men and 468 women. What is the margin of error for men and for women?When Americans eat out at restaurants, most choose American
19. Sunflowers In an article in the Annals of Botany, a researcher reported the basal stem diameters of two groups of sunflowers: those that were left to sway freely in the wind and those that were artificially supported.26 A similar experiment was conducted for maize plants.Although the authors
18. Eating Too Much? Partly because of our lifestyles and the availability of fast food, the average American consumes 15.4 kilograms of cheese, 5.5 kilograms of ice cream, and drinks 149.3 liters of soda each year.25 Suppose that we test the accuracy of these reported averages by selecting a
17. Audiology Research In a study to establish the absolute threshold of hearing, 70 male college freshmen were each seated in a soundproof room and a 150 H tone was presented at a large number of stimulus levels in a randomized order. The student was asked to press a button if he detected the
16. Ice Hockey, continued The mean and standard deviation of the speeds of the sample of 69 skaters at the end of the 6-meter distance in Exercise 14 were 5.753 and .892 meters per second, respectively.a. Find a 95% confidence interval for the mean velocity at the 6-meter mark. Interpret the
15. Ice Hockey, continued Refer to Exercise 14.The mean and standard deviation of the 69 individual average acceleration measurements over the 6-meter distance were 2.962 and .529 meters per second, respectively.a. Find a 95% confidence interval for this population mean. Interpret the interval.b.
14. Ice Hockey In an experiment related to “fast starts”—the acceleration and speed of a hockey player from a stopped position—sixty-nine hockey players, varsity and intramural, from the University of Illinois were required to move as rapidly as possible from a stopped position to cover a
13. Circuit Boards II Refer to Exercise 12. Suppose 10 samples of n5400 printed circuit boards were tested and a confidence interval was constructed for p for each of the 10 samples. What is the probability that exactly one of the intervals will not contain the true value of p? That at least one
12. Circuit Boards Samples of 400 printed circuit boards were selected from each of two production lines A and B. Line A produced 40 defectives, and line B produced 80 defectives. Estimate the difference in the actual fractions of defectives for the two lines with a confidence coefficient of .90.
11. Quality Control A quality-control engineer wants to estimate the fraction of defectives in a large lot of printer ink cartridges. From previous experience, he feels that the actual fraction of defectives should be somewhere around .05. How large a sample should he take if he wants to estimate
10. College Costs A dean of men wishes to estimate the average cost of the freshman year at a particular college correct to within $500, with a probability of .95.If a random sample of freshmen is to be selected and each asked to keep financial data, how many must be included in the sample? Assume
9. Fast Food! Even though we know it may not be good for us, many Americans really enjoy their fast food! A survey conducted by Pew Research Center23 graphically illustrated our eating habits, and in particular, our appetite for fast food:a. This survey was based on “telephone interviews
8. Heights If it is assumed that the heights of men are normally distributed with a standard deviation of 6.25 centimeters, how large a sample should be taken to be fairly sure (probability .95) that the sample mean does not differ from the true mean (population mean)by more than 1.25 in absolute
7. Iodine Concentration Based on repeated measurements of the iodine concentration in a solution, a chemist reports the concentration as 4.614, with an “error margin of .006.”a. How would you interpret the chemist’s “error margin”?b. If the reported concentration is based on a random
6. Smoking and Blood Pressure To study the effect of smoking on blood pressure, the blood pressure of a group of 35 cigarette smokers was measured at the beginning of an experiment and again 5 years later. The sample mean increase, measured in millimeters of mercury, was x 59.7, and the sample
5. Independent random samples of n 540 1 and n 580 2 observations were selected from binomial populations 1 and 2, respectively. The number of successes in the two samples were x 517 1 and x 523 2 .a. Find a 99% confidence interval for the difference between the two binomial population
4. A random sample of n5500 observations from a binomial population produced x5240 successes.a. Find a point estimate for p, and find the margin of error for your estimator.b. Find a 90% confidence interval for p. Interpret this interval.c. How large a sample is required if you wish to estimate p
3. Independent random samples of n 550 1 and n 560 2 observations were selected from populations 1 and 2, respectively. The sample sizes and computed sample statistics are given in the table:a. Find a 90% confidence interval for the difference in population means and interpret the interval.b.
2. A random sample of n564 observations has a mean x 529.1 and a standard deviation s53.9.a. Give the point estimate of the population mean m and find the margin of error for your estimate.b. Find a 90% confidence interval for m. What does“90% confident” mean?c. Find a 90% lower confidence
1. State the Central Limit Theorem. Of what value is the Central Limit Theorem in large-sample statistical estimation?
Use the data from Example 8.11 involving citizens opinions about a bond proposal, reproduced here.Find 99% confidence intervals for the proportion in the developing section favoring the proposal, and for the difference in the proportions favoring the proposal for the two sections of the city 1.
The tire wear of n 5n 5100 1 2 tires of two types in Example 8.9 had sample means and standard deviations shown in the table. Find an approximate 95% confidence interval for m1, the average tire wear for tire type 1, and a 95% confidence interval for the difference in the tire wear for the two
Use the data from Example 8.11 involving citizens opinions about a bond proposal, reproduced here.Find 99% confidence intervals for the proportion in the developing section favoring the proposal, and for the difference in the proportions favoring the proposal for the two sections of the city.1.
The random sample of n550 male adults in Example 8.6 had an average of 756 grams of dairy products per day, with a sample standard deviation of 35 grams. Find an approximate 95% confidence interval for m, the average daily intake of dairy products for all male adults.1. Select Stat ➤ Basic
16. Selenium, again Refer to Exercise 11 in Section 8.4.You want to compare the daily adult intake of the trace element selenium in two different regions of the United States and you want your estimate to be correct to within 5 micrograms, with probability equal to .90. If you plan to select an
15. GPA s You want to estimate the difference in grade point averages between two groups of college students accurate to within .2 grade point, with probability approximately equal to .95. If the standard deviation of the grade point measurements is approximately equal to.6, how many students must
14. pH in Rainfall Refer to Exercise 13. Suppose you wish to estimate the difference between the mean acidity for rainfalls at two different locations, one in a relatively unpolluted area and the other in an area subject to heavy air pollution. If you wish your estimate to be correct to the nearest
13. Polluted Rain Suppose you wish to estimate the mean pH of rainfalls in a heavily polluted area. You know that s is approximately .5 pH, and you wish your estimate to lie within .1 of m, with a probability near .95.Approximately how many rainfalls must be included in your sample (one pH reading
12. Hunting Season A wildlife service wishes to estimate the mean number of days of hunting per hunter for all hunters licensed in the state during a given season.How many hunters must be included in the sample in order to estimate the mean with a bound on the error of estimation equal to 2 hunting
11. Political Corruption A questionnaire is designed to investigate attitudes about political corruption in government. The experimenter would like to survey two different groups—Republicans and Democrats—and compare the responses to various “yes/no” questions for the two groups. The
10. Illegal Immigration Suppose that you were designing a research poll that included questions about illegal immigration into the United States, and the federal and state responses to the problem.a. Explain how you would select your sample. What problems might you encounter in this process?b. If
9. Ethnic Cuisine Ethnic groups in America buy differing amounts of various food products because of their ethnic cuisine. A researcher interested in market segmentation for Asian and Hispanic households would like to estimate the proportion of households that select certain brands for various
8. The Citrus Red Mite, continued A grower believes that one in five of his citrus trees are infected with the citrus red mite mentioned in Exercise 7. How large a sample should be taken if the grower wishes to estimate the proportion of his trees that are infected with citrus red mite to within
7. The Citrus Red Mite An entomologist wishes to estimate the average development time of the citrus red mite, a small spider-like insect that causes damage to leaves and fruit, correct to within .5 day. From previous experiments it is known that s is approximately 4 days.How large a sample should
6. Estimating p 2 p 1 2 to within .05 with probability.98. Assume that the sample sizes will be equal, but that you have no prior knowledge about the values of p1 and p2. Suppose you want to estimate one of four parameters—m, m 2m , , 2 1 2 1 2 p or p p —to within a given bound with a certain
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