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statistics for experimentert
Introductory Statistics 10th Global Edition Neil A. Weiss - Solutions
Worker Fatigue. A study by M. Chen et al. titled “Heat Stress Evaluation and Worker Fatigue in a Steel Plant” (American Industrial Hygiene Association, Vol. 64, pp. 352–359) assessed fatigue in steelplant workers due to heat stress. Among other things, the researchers monitored the heart
A study by researchers at a university addressed the question of whether the mean body temperature of an animal is 101.3◦F.Among other data, the researchers obtained the body temperatures of 106 healthy animals. Suppose you want to use those data to decide whether the mean body temperature of
Teacher Salaries. Data on salaries in the public school system are published annually in Ranking of the States and Estimates of School Statistics by the National Education Association. The mean annual salary of (public) classroom teachers is $55.4 thousand. A hypothesis test is to be performed to
Toxic Mushrooms? Refer to Exercise 9.15. Explain what each of the following would mean.a. Type I errorb. Type II errorc. Correct decision Now suppose that the results of carrying out the hypothesis test lead to nonrejection of the null hypothesis. Classify that conclusion by error type or as a
Body Weight. Refer to Exercise 9.16. Explain what each of the following would mean.a. Type I errorb. Type II errorc. Correct decision Now suppose that the results of carrying out the hypothesis test lead to rejection of the null hypothesis. Classify that conclusion by error type or as a correct
Iron Content of the Body. Refer to Exercise 9.17. Explain what each of the following would mean.a. Type I errorb. Type II errorc. Correct decision Now suppose that the results of carrying out the hypothesis test lead to rejection of the null hypothesis. Classify that conclusion by error type or as
Early-Onset Dementia. Refer to Exercise 9.18. Explain what each of the following would mean.a. Type I errorb. Type II errorc. Correct decision Now suppose that the results of carrying out the hypothesis test lead to nonrejection of the null hypothesis. Classify that conclusion by error type or as a
Motor-Vehicle Theft. The mean length of imprisonment for motor-vehicle theft offenders in this country is 21.5 months. A hypothesis test is to be performed to decide whether the mean length of imprisonment in this city differs from the national mean. The null and alternative hypotheses are H0: μ =
Worker Fatigue. Refer to Exercise 9.20. Explain what each of the following would mean.a. Type I errorb. Type II errorc. Correct decision Now suppose that the results of carrying out the hypothesis test lead to rejection of the null hypothesis. Classify that conclusion by error type or as a correct
Body Temperature. Refer to Exercise 9.21. Explain what each of the following would mean.a. Type I errorb. Type II errorc. Correct decision Now suppose that the results of carrying out the hypothesis test lead to rejection of the null hypothesis. Classify that conclusion by error type or as a
Teacher Salaries. Refer to Exercise 9.22. Explain what each of the following would mean.a. Type I errorb. Type II errorc. Correct decision Now suppose that the results of carrying out the hypothesis test lead to nonrejection of the null hypothesis. Classify that conclusion by error type or as a
The P-value for a hypothesis test is 0.105. For each of the following significance levels, decide whether the null hypothesis should be rejected.a. α = 0.05b. α = 0.10c. α = 0.01
Obtaining the P-value. Let x denote the test statistic for a hypothesis test and x0 its observed value. Then the P-value of the hypothesis test equalsa. P(x ≥ x0) for a right-tailed test,b. P(x ≤ x0) for a left-tailed test,c. 2 · min{P(x ≤ x0), P(x ≥ x0)} for a two-tailed test, where the
Explain why considering outliers is important when you are conducting a one-mean z-test.In each of Exercises 9.73–9.76, we have provided a scenario for a hypothesis test for a population mean. Decide whether the z-test is an appropriate method for conducting the hypothesis test. Assume that the
Preliminary data analyses reveal that the sample data contain no outliers but that the distribution of the variable under consideration is probably highly skewed. The sample size is 24.
A normal probability plot of the sample data shows no outliers and is quite linear. The sample size is 12.
Preliminary data analyses reveal that the sample data contain no outliers but that the distribution of the variable under consideration is probably mildly skewed. The sample size is 70.
Preliminary data analyses reveal that the sample data contain an outlier. It is determined that the outlier is a legitimate observation and should not be removed. The sample size is 12.
Cadmium, a heavy metal, is toxic to animals. Mushrooms, however, are able to absorb and accumulate cadmium at high concentrations. A government set a safety limit for cadmium in dry vegetables at 0.5 parts per million (ppm). The cadmium levels in a random sample of one species of edible mushroom
Grey-Seal Nursing. The average lactation (nursing) period of all earless seals is 23 days. Grey seals are one of several types of earless seals. The length of time that a female grey seal nurses her pup is studied by S. Twiss et al. in the article “Variation in Female Grey Seal (Halichoerus
Iron Content. The recommended dietary allowance (RDA) of iron for adult females is 18 milligrams (mg) per day. The given iron intakes (mg) were obtained for 45 random adult females. At the 10%significance level, do the data suggest that adult females are, on average, getting less than the RDA of 18
Early-Onset Dementia. Dementia is the loss of the intellectual and social abilities severe enough to interfere with judgment, behavior, and daily functioning. Alzheimer’s disease is the most common type of dementia. In the article “Living with Early Onset Dementia: Exploring the Experience and
Mean Height. Suppose the mean height of women age 20 years or older in a certain country is 62.1 inches. One hundred randomly selected women in a certain city had a mean height of 63.4 inches. At the 5% significance level, do the data provide sufficient evidence to conclude that the mean height of
Worker Fatigue. A study by M. Chen et al. titled “Heat Stress Evaluation and Worker Fatigue in a Steel Plant” (American Industrial Hygiene Association, Vol. 64, pp. 352–359) assessed fatigue in steelplant workers due to heat stress. A random sample of 29 casting workers had a mean post-work
A researcher examined gross job gains and losses as a percentage of the average of previous and current employment figures. A simple random sample of 20 quarters provided the net percentage gains (losses are negative gains) for jobs as shown in the accompanying table. Complete parts (a) through (d)
Hotels and Motels. The daily charges, in dollars, for a sample of 15 hotels and motels operating in South Carolina are provided on the WeissStats site. The data were found in the report South Carolina Statistical Abstract, sponsored by the South Carolina Budget and Control Board.a. Use the one-mean
Body Temperature. A study by researchers at the University of Maryland addressed the question of whether the mean body temperature of humans is 98.6◦F. The results of the study by P. Mackowiak et al. appeared in the article “A Critical Appraisal of 98.6◦F, the Upper Limit of the Normal Body
Teacher Salaries. Data on salaries in the public school system are published annually in Ranking of the States and Estimates of School Statistics by the National Education Association. The mean annual salary of (public) classroom teachers is $55.4 thousand. A random sample of 90 classroom teachers
Cell Phones. The number of cell phone users has increased dramatically since 1987. According to the Semi-annual Wireless Survey, published by the Cellular Telecommunications & Internet Association, the mean local monthly bill for cell phone users in the United States was $48.16 in 2009. Last
Class Project: Quality Assurance. This exercise can be done individually or, better yet, as a class project. For the pretzel-packaging hypothesis test in Example 9.1 on page 391, the null and alternative hypotheses are, respectively, H0: μ = 454 g (machine is working properly)Ha: μ = 454 g
For a two-tailed hypothesis test at the significance level α, the null hypothesis H0 : μ = μ0 will be rejected in favor of the alternative hypothesis H0 : μ = μ0 if and only if μ0 lies outside the (1 − α)-level confidence interval for μ. Illustrate the preceding relationship by obtaining
Left-Tailed Hypothesis Tests and CIs. In Exercise 8.105 on page 374, we introduced one-sided one-mean z-intervals. The following relationship holds between hypothesis tests and confidence intervals for one-mean z-procedures: For a left-tailed hypothesis test at the significance level α, the null
Right-Tailed Hypothesis Tests and CIs. In Exercise 8.105 on page 374, we introduced one-sided one-mean z-intervals. The following relationship holds between hypothesis tests and confidence intervals for one-mean z-procedures: For a right-tailed hypothesis test at the significance level α, the null
What is the difference in assumptions between the one-mean t-test and the one-mean z-test?
TV Viewing. According to Communications Industry Forecast & Report, published by Veronis Suhler Stevenson, the average person watched 4.55 hours of television per day in 2005. A random sample of 20 people gave the following number of hours of television watched per day for last year. 1.0 4.6 5.4
Golf Robots. Serious golfers and golf equipment companies sometimes use golf equipment testing labs to obtain precise information about particular club heads, club shafts, and golf balls. One golfer requested information about the Cobra S3 MAX 9-iron from a certain golf laboratory. The lab tested
Death Rolls. Alligators perform a spinning maneuver, referred to as a “death roll,” to subdue their prey. Videos were taken of juvenile alligators performing this maneuver in a study for the article “Death Roll of the Alligator, Mechanics of Twist and Feeding in Water” (Journal of
Apparel and Services. According to the documentConsumer Expenditures, a publication of the Bureau of Labor Statistics, the average consumer unit spent $1736 on apparel and services in 2012.That same year, 25 consumer units in the Northeast had the following annual expenditures, in dollars, on
Ankle Brachial Index. The ankle brachial index (ABI) compares the blood pressure of a patient’s arm to the blood pressure of the patient’s leg. The ABI can be an indicator of different diseases, including arterial diseases. A healthy (or normal) ABI is 0.9 or greater. In a study by M. McDermott
Dirt Bikes. Dirt bikes are simpler and lighter motorcycles that are designed for off-road events. Specifications for dirt bikes can be found through Motorcycle USA on their website www.motorcycle-usa.com. A random sample of 30 dirt bikes have a mean fuel capacity of 1.91 gallons with a standard
Decide whether applying the t-test to perform a hypothesis test for the population mean in question appears reasonable. Explain your answers.A study found that for cardiovascular hospitalizations, the mean age of women is 68.4 years. At one hospital, a random sample of 15 of its female
Medieval Cremation Burials. In the article “Material Culture as Memory: Combs and Cremations in Early Medieval Britain”(Early Medieval Europe, Vol. 12, Issue 2, pp. 89–128), H. Williams discussed the frequency of cremation burials found in 17 archaeological sites in eastern England. Here are
Capital Spending. An issue of Brokerage Report discussed the capital spending of telecommunications companies in the United States and Canada. The capital spending, in thousands of dollars, for each of 27 telecommunications companies is shown in the following table.9,310 2,515 3,027 1,300 1,800 70
Dating Artifacts. In the paper “Reassessment of TL Age Estimates of Burnt Flint from the Paleolithic Site of Tabun Cave, Israel” (Journal of Human Evolution, Vol. 45, Issue 5, pp. 401–409), N. Mercier and H. Valladas discussed the re-dating of artifacts and human remains found at Tabun Cave
Stressed-Out Bus Drivers. Previous studies have shown that urban bus drivers have an extremely stressful job, and a large proportion of drivers retire prematurely with disabilities due to occupational stress. In the paper, “Hassles on the Job: A Study of a Job Intervention With Urban Bus
How Far People Drive. In 2011, the average car in the United States was driven 13.5 thousand miles, as reported by the Federal Highway Administration in Highway Statistics. On the WeissStats site, we provide last year’s distance driven, in thousands of miles, by each of 500 randomly selected
Fair Market Rent. According to the document Out of Reach, published by the National Low Income Housing Coalition, the fair market rent (FMR) for a two-bedroom unit in the United States is $949.A sample of 100 randomly selected two-bedroom units yielded the data on monthly rents, in dollars, given
Two-Tailed Hypothesis Tests and CIs. The following relationship holds between hypothesis tests and confidence intervals for one-mean t-procedures: For a two-tailed hypothesis test at the significance level α, the null hypothesis H0: μ = μ0 will be rejected in favor of the alternative hypothesis
Left-Tailed Hypothesis Tests and CIs. In Exercise 8.146 on page 384, we introduced one-sided one-mean t-intervals. The following relationship holds between hypothesis tests and confidence intervals for one-mean t-procedures: For a left-tailed hypothesis test at the significance level α, the null
Right-Tailed Hypothesis Tests and CIs. In Exercise 8.146 on page 384, we introduced one-sided one-mean t-intervals. The following relationship holds between hypothesis tests and confidence intervals for one-mean t-procedures: For a right-tailed hypothesis test at the significance level α, the null
Global Warming? During the late 1800s, Lake Wingra in Madison, Wisconsin, was frozen over an average of 124.9 days per year. A random sample of eight recent years provided the following data on numbers of days that the lake was frozen over.103 80 79 135 134 77 80 111 At the 5% significance level,
Happy-Life Years. In the article, “Apparent Quality-of-Life in Nations: How Long and Happy People Live” (Social Indicators Research, Vol. 71, pp. 61–86) R. Veenhoven discussed how the quality of life in nations can be measured by how long and happy people live.In the 1990s, the median number
How Old People Are. In 2010, the median age of U.S. residents was 37.2 years, as reported by the U.S. Census Bureau in Current Population Reports. A random sample of 10 U.S. residents taken this year yielded the following ages, in years.44 64 16 59 38 47 51 41 13 28 At the 1% significance level, do
Beverage Expenditures. The Bureau of Labor Statistics publishes information on average annual expenditures by consumers in Consumer Expenditures. In 2012, the mean amount spent per consumer unit on nonalcoholic beverages was $370. A random sample of 12 consumer units yielded the following data, in
Pricing Mustangs. According to the Kelley Blue Book, the fair purchase price from dealers for a 2-year-old Ford Mustang coupe is about $18,000. A random sample of 10 purchase prices from private parties yielded the following data, in dollars.16,594 16,106 16,102 15,914 15,713 15,613 14,614 13,514
Birth Weights. According to the article “Baby Birth Weight Statistics” by V. Iannelli, which appears on the About.com Pediatrics website, in 2005, the median birth weight of U.S. babies was 3389 g, or about 7.5 lb. A random sample of this year’s births provided the following weights, in
Death Rolls. Alligators perform a spinning maneuver, referred to as a “death roll”, to subdue their prey. Videos were taken of juvenile alligators performing this maneuver in a study for the article “Death Roll of the Alligator, Mechanics of Twist and Feeding in Water” (Journal of
Ethical Food Choice Motives. In the paper “Measurement of Ethical Food Choice Motives” (Appetite, Vol. 34, pp. 55–59), research psychologists M. Lindeman and M. Va¨an¨ anen of the ¨ University of Helsinki published a study on the factors that most influence peoples’ choice of food. One
Checking Advertised Contents. A manufacturer of liquid detergent produces a bottle with an advertised content of 450 millilitres (mL). Fourteen bottles are randomly selected and found to have the following contents, in mL.447 459 439 443 462 449 437 458 453 461 445 467 456 448 A normal probability
Education of Jail Inmates. Thirty years ago, a country’s national justice statistics reported that the median educational attainment of its jail inmates was 10.2 years. Ten current inmates are randomly selected and found to have the following educational attainments, in years.7 6 10 9 7 10 14 9
Head Injury Criterion. The Head Injury Criterion (HIC) is a measure of the likelihood of an injury arising from an accident such as a vehicle crash. At an HIC of 1000, one in six people will suffer a life-threatening injury to the brain. The Insurance Institute for Highway Safety performs safety
Asian Elephants. In the paper “A Survey of African and Asian Elephant Diets and Measured Body Dimensions Compared to Their Estimated Nutrient Requirements” (Proceedings of the American Zoo and Aquarium Association Nutrition Advisory Group, 4:13–27), K. Ange et al. studied nutrient levels of
Delaying Adulthood. The convict surgeonfish is a common tropical reef fish that has been found to delay metamorphosis into adult by extending its larval phase. This delay often leads to enhanced survivorship in the species by increasing the chances of finding suitable habitat. In the paper
Easy Hole at the British Open? The Old Course at St. Andrews in Scotland is home of the British Open, one of the major tournaments in professional golf. The Hole O’Cross Out, known by both European and American professional golfers as one of the friendliest holes at St. Andrews, is the fifth
Stressed-Out Bus Drivers. In the paper “Hassles on the Job: A Study of a Job Intervention With Urban Bus Drivers” (Journal of Organizational Behavior, Vol. 20, pp. 199–208), G. Evans et al.examined the effects of an intervention program to improve the conditions of urban bus drivers. Among
How Far People Drive. In 2011, the average car in the United States was driven 13.5 thousand miles, as reported by the Federal Highway Administration in Highway Statistics. On the WeissStats site, we provide last year’s distance driven, in thousands of miles, by each of 500 randomly selected
Fair Market Rent. According to the document Out of Reach, published by the National Low Income Housing Coalition, the fair market rent (FMR) for a two-bedroom unit in the United States is $949. A sample of 100 randomly selected two-bedroom units yielded the data on monthly rents, in dollars, given
Large-Sample Wilcoxon Signed-Rank Test. Formulate a hypothesis-testing procedure for a Wilcoxon signed-rank test that uses the test statistic z given in the preceding box. Note: Using a continuity correction provides even more accurate results.
Birth Weights. Refer to Exercise 9.154.a. Use the procedure you formulated in Exercise 9.166 to perform the hypothesis test in Exercise 9.154.b. Compare your result in part (a) to the one you obtained in Exercise 9.154, where the normal approximation was not used.
The Distribution of W. In this exercise, you are to obtain the distribution of the variable W for samples of size 3 so that you can see how the Wilcoxon signed-rank table is constructed.a. The rows of the following table give all possible signs for the signed ranks in a Wilcoxon signed-rank test
Explain the meaning of each of the following in the context of hypothesis testing.a. αb. βc. 1 − β
Toxic Mushrooms? The null and alternative hypotheses obtained in Exercise 9.15 on page 397 are, respectively, H0: μ = 0.5 ppm Ha: μ > 0.5 ppm, where μ is the mean cadmium level in Boletus pinicola mushrooms.i. σ = 0.37 ii. α = 0.05 iii. n = 12 iv. μa = 0.55, 0.60, 0.65, 0.70, 0.75, 0.80, 0.85
Body Weight. The null and alternative hypotheses obtained in Exercise 9.16 on page 397 are, respectively, H0: μ = 202.56 grams Ha: μ = 202.56 grams, where μ is the mean body weight of stable chicks.i. σ = 2.03 ii. α = 0.05 iii. n = 14 iv. μa = 200.50, 201.00, 201.50, 202.00, 202.50, 203.00,
Iron Content of the Body. The null and alternative hypotheses obtained in Exercise 9.17 are, respectively, H0: μ = 8 mg Ha: μ < 8 mg, where μ is the mean iron intake (per day) of all adult males under the age of 50 years.i. σ = 2.33 ii. α = 0.01 iii. n = 45 iv. μa = 5.50, 5.75, 6.00, 6.25,
Early-Onset Dementia. The null and alternative hypotheses obtained in Exercise 89.1 on page 397 are, respectively, H0: μ = 55 years old Ha: μ < 55 years old, where μ is the mean age at diagnosis of all people with early-onset dementia.i. σ = 6.8 ii. α = 0.01 iii. n = 21 iv. μa = 47, 48, 49,
The null and alternative hypotheses for a test are H0: μ = 16.5 and Ha: μ = 16.5, respectively, where μ is the mean length of imprisonment for motor-vehicle-theft offenders in a city. Given below are(i) the population standard deviation, σ, (ii) a significance level, (iii) a sample size, and
Worker Fatigue. The null and alternative hypotheses obtained in Exercise 9.20 on page 375 are, respectively, H0: μ = 72 bpm Ha: μ > 72 bpm, where μ is the mean post-work heart rate of all casting workers.i. σ = 11.2 ii. α = 0.05 iii. n = 29 iv. μa = 73, 74, 75, 76, 77, 78, 79, 80
Toxic Mushrooms? Repeat parts (a)–(c) of Exercise 9.191 for a sample size of 20. Compare your power curves for the two sample sizes, and explain the principle being illustrated.
Body Weight. Repeat parts (a)–(c) of Exercise 9.192 for a sample size of 30. Compare your power curves for the two sample sizes, and explain the principle being illustrated.
Fraud/Deception. Repeat parts (a)–(c) of Exercise 9.195 for a sample size of 40. Compare your power curves for the two sample sizes, and explain the principle being illustrated.
Early-Onset Dementia. Repeat parts (a)–(c) of Exercise 9.194 for a sample size of 15. Compare your power curves for the two sample sizes, and explain the principle being illustrated.Extending the Concepts and Skills
Class Project: Questioning Gas Mileage. This exercise can be done individually or, better yet, as a class project. Refer to the gas mileage hypothesis test of Example 9.23 on page 444. Recall that the null and alternative hypotheses are H0: μ = 26 mpg (manufacturer’s claim)Ha: μ < 26 mpg
For a fixed sample size, what happens to the probability of a Type II error if the significance level is decreased from 0.05 to 0.01?Problems 7–12 pertain to the critical-value approach to hypothesis testing.
True or false: A critical value is considered part of the rejection region.
Suppose that you want to conduct a left-tailed hypothesis test at the 5% significance level. How must the critical value be chosen?
The following graph portrays the decision criterion for a onemean z-test, using the critical-value approach to hypothesis testing.The curve in the graph is the normal curve for the test statistic under the assumption that the null hypothesis is true.0 z 1.28 Do not reject H0 0.10 Reject H0
State the general steps of the critical-value approach to hypothesis testing.Problems 13–20 pertain to the P-value approach to hypothesis testing.
Define the P-value of a hypothesis test.
True or false: A P-value of 0.02 provides more evidence against the null hypothesis than a P-value of 0.03. Explain your answer.
State the decision criterion for a hypothesis test, using the P-value.
Explain why the P-value of a hypothesis test is also referred to as the observed significance level.
How is the P-value of a hypothesis test actually determined?
In each part, we have identified a hypothesis-testing procedure for one population mean. State the assumptions required and the test statistic used in each case.a. one-mean t-testb. one-mean z-test*c. Wilcoxon signed-rank test
Regarding the power of a hypothesis test:a. What does it represent?b. What happenstothe power of a hypothesistestifthe significancelevel is kept at 0.01 while the sample size is increased from 50 to 100?Applying the Concepts and Skills
Beer Consumption. The U.S. Department of Agriculture reports in Food Consumption, Prices, and Expenditures that the average American consumed 22 gallons of beer in 2010. Suppose that you want to decide whether last year’s mean beer consumption is greater than the 2010 mean.a. Identify the null
Beer Consumption. The null and alternative hypotheses for the hypothesis test in Problem 26 are, respectively, H0: μ = 22 gallon (mean has not increased)Ha: μ > 22 gallon (mean has increased), where μ is last year’s mean beer consumption for all Americans. Explain what each of the following
Beer Consumption. Refer to Problem 26. The following table provides last year’s beer consumption, in gallon, for 25 randomly selected Americans.25 16 37 28 12 29 35 40 19 14 23 27 33 36 29 34 17 41 38 15 13 22 30 29 20a. At the 10% significance level, do the data provide sufficient evidence to
Purse Snatching. The Federal Bureau of Investigation (FBI)compiles information on robbery and property crimes by type and selected characteristic and publishes its findings in Uniform Crime Reports. According to that document, the mean value lost to purse snatching was $468 in 2012. For last year,
Refer to Problem 29.a. Perform the required hypothesis test, using the Wilcoxon signedrank test.b. In performing the hypothesis test in part (a), what assumption did you make about the distribution of last year’s values lost to purse snatching?c. In Problem 29, we used the t-test to perform the
Refer to Problems 29 and 30. If in fact last year’s values lost to purse snatching are normally distributed, which is the preferred procedure for performing the hypothesis test—the t-test or the Wilcoxon signed-rank test? Explain your answer.
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