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statistics alive

Questions and Answers of Statistics Alive

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
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,
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
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
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
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
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
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
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
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
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
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
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
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?
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
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
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
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.
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
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
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.
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
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
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
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
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
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
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
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%
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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 ,
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 ,
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
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
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
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
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
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
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
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
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,
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
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;
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
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
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
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
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,
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,
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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

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