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Understanding Basic Statistics 6th Edition Charles Henry Brase, Corrinne Pellillo Brase - Solutions
Solve Problem 13 using the critical region method of testing. Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same?
Solve Problem 14 using the critical region method of testing. Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same?
Consider a test for μ. If the P-value is such that you can reject H0 at the 5% level of significance, can you always reject H0 at the 1% level of significance? Explain.
If sample data are such that for a one-tailed test of μ you can reject H0 at the 1% level of significance, can you always reject H0 for a two-tailed test at the same level of significance? Explain.
For a Student’s t distribution with d.f. = 10 and t = 2.930: (a) Find an interval containing the corresponding P-value for a two-tailed test. (b) Find an interval containing the corresponding P-value for a right-tailed test.
For a Student’s t distribution with d.f. = 16 and t = 21.830: (a) Find an interval containing the corresponding P-value for a two-tailed test. (b) Find an interval containing the corresponding P-value for a left-tailed test.
A random sample of 25 values is drawn from a mound-shaped and symmetrical distribution. The sample mean is 10 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 9.5. (a) Is it appropriate to use a
Women athletes at the University of Colorado at Boulder have a long-term graduation rate of 67%. Over the past several years, a random sample of 38 women athletes at the school showed that 21 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from
The U.S. Department of Transportation’s National Highway Traffic Safety Administration reported that 77% of all fatally injured automobile drivers were intoxicated. A random sample of 27 records of automobile driver fatalities in Kit Carson County, Colorado, showed that 15 involved an intoxicated
What is your favorite color? A large survey of countries, including the United States, China, Russia, France, Turkey, Kenya, and others, indicated that most people prefer the color blue. In fact, about 24% of the population claim blue as their favorite color. Suppose a random sample of n = 56
The following is based on information from The Wolf in the Southwest: The Making of an Endangered Species by David E. Brown (University of Arizona Press). Before 1918, the proportion of female wolves in the general population of all Southwestern wolves was about 50%. However, after 1918,
Blackmur’s Athabasca Fishing Lodges is located on Lake Athabasca in northern Canada. In one of its recent brochures, the lodge advertises that 75% of its guests catch northern pike over 20 pounds. Suppose that last summer 64 out of a random sample of 83 guests did, in fact, catch northern pike
Prose rhythm is characterized by the occurrence of five-syllable sequences in long passages of text. This characterization may be used to assess the similarity among passages of text and sometimes the identity of authors. The following information is based on an article by D. Wishart and S. V.
Symposium is part of a larger work referred to as Plato’s Dialogues. Wishart and Leach found that about 21.4% of five-syllable sequences in Symposium are of the type in which four are short and one is long. Suppose an antiquities store in Athens has a very old manuscript that the owner claims is
USA Today reported that about 47% of the general consumer population in the United States is loyal to the automobile manufacturer of their choice. Suppose Chevrolet did a study of a random sample of 1006 Chevrolet owners and found that 490 said they would buy another Chevrolet. Does this indicate
Harper’s Index reported that 80% of all supermarket prices end in the digit 9 or 5. Suppose you check a random sample of 115 items in a supermarket and find that 88 have prices that end in 9 or 5. Does this indicate that less than 80% of the prices in the store end in the digits 9 or 5? Use α =
This problem is based on information taken from The Merck Manual (a reference manual used in most medical and nursing schools). Hypertension is defined as a blood pressure reading over 140 mm Hg systolic and/or over 90 mm Hg diastolic. Hypertension, if not corrected, can cause long-term health
Consider a binomial experiment with n trials and r successes. For a test for a proportion p, what is the formula for the sample test statistic? Describe each symbol used in the formula.
Diltiazem is a commonly prescribed drug for hypertension. However, diltiazem causes headaches in about 12% of patients using the drug. It is hypothesized that regular exercise might help reduce the headaches. If a random sample of 209 patients using diltiazem exercised regularly and only 16 had
Are most student government leaders extroverts? According to Myers-Briggs estimates, about 82% of college student government leaders are extroverts. Suppose that a Myers-Briggs personality preference test was given to a random sample of 73 student government leaders attending a large national
Solve Problem 9 using the critical region method of testing. Since the sampling distribution of is the normal distribution, you can use critical values from the standard normal distribution as shown in Figure 9-8 or part (c) of Table 3 of the Appendix. Compare your conclusions with the conclusions
Solve Problem 11 using the critical region method of testing. Compare your conclusions with the conclusions obtained by using the P-value method. Are they the same?
Solve Problem 17 using the critical-region method of testing. Compare your conclusions with the conclusions obtained by using the P-value method. Are they the same?
An article in a newspaper states that the proportion of traffic accidents involving road rage is higher this year than it was last year, when it was 15%. Reconstruct the information of the study in terms of a hypothesis test. Discuss possible hypotheses, possible issues about the sample, possible
A random sample of 30 binomials trials resulted in 12 successes. Test the claim that the population proportion of successes does not equal 0.50. Use a level of significance of 0.05. (a) Can a normal distribution be used for the distribution? Explain. (b) State the hypotheses. (c) Compute and
A random sample of 60 binomials trials resulted in 18 successes. Test the claim that the population proportion of successes exceeds 18%. Use a level of significance of 0.01. (a) Check Requirements Can a normal distribution be used for the distribution? Explain. (b) State the hypotheses. (c)
Please read the Focus Problem at the beginning of this chapter. Recall that Benford’s Law claims that numbers chosen from very large data files tend to have “1” as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very
Again, suppose you are the auditor for a very large corporation. The revenue file contains millions of numbers in a large computer data bank (see Problem 7). You draw a random sample of n = 228 numbers from this file and r = 92 have a first nonzero digit of 1. Let p represent the population
Is the national crime rate really going down? Some sociologists say yes! They say that the reason for the decline in crime rates in the 1980s and 1990s is demographics. It seems that the population is aging, and older people commit fewer crimes. According to the FBI and the Justice Department, 70%
When testing μ, how do we decide whether to use the standard normal distribution or a Student’s t distribution?
The Congressional Budget Office reports that 36% of federal civilian employees have a bachelor’s degree or higher (The Wall Street Journal). A random sample of 120 employees in the private sector showed that 33 have a bachelor’s degree or higher. Does this indicate that the percentage of
A machine in the student lounge dispenses coffee. The average cup of coffee is supposed to contain 7.0 ounces. Eight cups of coffee from this machine show the average content to be 7.3 ounces with a standard deviation of 0.5 ounce. Do you think that the machine has slipped out of adjustment and
The manufacturer of a sports car claims that the fuel injection system lasts 48 months before it needs to be replaced. A consumer group tests this claim by surveying a random sample of 10 owners who had the fuel injection system replaced. The ages of the cars at the time of replacement were (in
Based on information in the Statistical Abstract of the United States (116th edition), the average annual miles driven per vehicle in the United States is 11.1 thousand miles, with σ ≈ 600 miles. Suppose that a random sample of 36 vehicles owned by residents of Chicago showed that the average
Professor Jennings claims that only 35% of the students at Flora College work while attending school. Dean Renata thinks that the professor has underestimated the number of students with part-time or fulltime jobs. A random sample of 81 students shows that 39 have jobs. Do the data indicate that
The Toylot Company makes an electric train with a motor that it claims will draw an average of only 0.8 ampere (A) under a normal load. A sample of nine motors was tested, and it was found that the mean current was = 1.4 A, with a sample standard deviation of s = 0.41 A. Do the data indicate that
The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches per box, with σ = 9. A random sample of 94 Nero matchboxes shows the average number of matches per box to be 43.1. Using a 1% level of significance, can you say that the average number of matches per box is
A hospital reported that the normal death rate for patients with extensive burns (more than 40% of skin area) has been significantly reduced by the use of new fluid plasma compresses. Before the new treatment, the mortality rate for extensively burned patients was about 60%. Using the new
Is fishing better from a boat or from the shore? Pyramid Lake is located on the Paiute Indian Nation in Nevada. Presidents, movie stars, and people who just want to catch fish go to Pyramid Lake for really large cutthroat trout. Let row B represent hours per fish caught fishing from the shore, and
The following is based on information taken from Winter Wind Studies in Rocky Mountain National Park, by D. E. Glidden (Rocky Mountain Nature Association). At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are
The western United States has a number of four-lane interstate highways that cut through long tracts of wilderness. To prevent car accidents with wild animals, the highways are bordered on both sides with 12-foot-high woven wire fences. Although the fences prevent accidents, they also disturb the
In environmental studies, sex ratios are of great importance. Wolf society, packs, and ecology have been studied extensively at different locations in the U.S. and foreign countries. Sex ratios for eight study sites in northern Europe are shown below (based on The Wolf by L. D. Mech, University of
In the following data pairs, A represents birth rate and B represents death rate per 1000-resident population. The data are paired by counties in the Midwest. A random sample of 16 counties gave the following information:Do the data indicate a difference (either way) between population average
Do professional golfers play better in their first round? Let row B represent the score in the fourth (and final) round, and let row A represent the score in the first round of a professional golf tournament. A random sample of finalists in the British Open gave the following data for their first
The following is based on information taken from Bandelier Archaeological Excavation Project: Summer 1990 Excavations at Burnt Mesa Pueblo and Casa del Rito, edited by T. A. Kohler (Washington State University, Department of Anthropology). The artifact frequency for an excavation of a kiva in
In the following data pairs, A represents the cost of living index for housing and B represents the cost of living index for groceries. The data are paired by metropolitan areas in the United States. A random sample of 36 metropolitan areas gave the following information:i. Let d be the random
Using techniques from Section 8.2, we can find a confidence interval for μd. Consider a random sample of n matched data pairs A, B. Let d = B - A be a random variable representing the difference between the values in a matched data pair. Compute the sample mean of the differences and
Solve Problem 9 using the critical region method of testing. Compare your conclusions with the conclusion obtained by using the P-value method. Are they the same?
Solve Problem 11 using the critical region method of testing. Compare your conclusions with the conclusion obtained by using the P-value method. Are they the same?
For a random sample of 36 data pairs, the sample mean of the differences was 0.8. The sample standard deviation of the differences was 2. At the 5% level of significance, test the claim that the population mean of the differences is different from 0. (a) Is it appropriate to use a Student’s t
For a random sample of 20 data pairs, the sample mean of the differences was 2. The sample standard deviation of the differences was 5. Assume that the distribution of the differences is mound-shaped and symmetrical. At the 1% level of significance, test the claim that the population mean of the
Are Americas top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at row B, the annual company percentage increase in revenue, versus row A, the CEOs annual percentage salary increase in that same company. A random
Two populations have normal distributions. The first has population standard deviation 2 and the second has population standard deviation 3. A random sample of 16 measurements from the first population had a sample mean of 20. An independent random sample of 9 measurements from the second
REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have more REM sleep than adults. Assume that REM sleep time is normally distributed for both children and adults. A random sample of n1 =
Based on information from the Rocky Mountain News, a random sample of n1 = 12 winter days in Denver gave a sample mean pollution index of 1 = 43. Previous studies show that σ1 = 21. For Englewood (a suburb of Denver), a random sample of n2 = 14 winter days gave a sample mean pollution index of 2
A Michigan study concerning preference for outdoor activities used a questionnaire with a six-point Likert-type response in which 1 designated “not important” and 6 designated “extremely important.” A random sample of n1 = 46 adults were asked about fishing as an outdoor activity. The mean
Education influences attitude and lifestyle. Differences in education are a big factor in the “generation gap.” Is the younger generation really better educated? Large surveys of people age 65 and older were taken in n1 = 32 U.S. cities. The sample mean for these cities showed that 1 = 15.2%
A random sample of n1 = 10 regions in New England gave the following violent crime rates (per million population):x1: New England crime rateAnother random sample of n2 = 12 regions in the Rocky Mountain states gave the following violent crime rates (per million population): x2: Rocky Mountain
A random sample of n1 = 16 communities in western Kansas gave the following information for people under 25 years of age:x1: Rate of hay fever per 1000 population for people under 25A random sample of n2 = 14 regions in western Kansas gave the following information for people over 50 years old: x2:
In the journal American Journal on Intellectual and Developmental Disabilities, an article reported the results of a peer tutoring program to help mildly mentally retarded children learn to read. In the experiment, the mildly retarded children were randomly divided into two groups: The experimental
In the article cited in Problem 17, the results of the following experiment were reported: Form 2 of the Gates-MacGintie Reading Test was administered to both an experimental group and a control group after 6 weeks of instruction during which the experimental group received peer tutoring and the
A study of fox rabies in southern Germany gave information about different regions and the occurrence of rabies in each region. Based on information from this article, a random sample of n1 = 16 locations in region I gave the following information about the number of cases of fox rabies near that
The pathogen Phytophthora capsici causes bell peppers to wilt and die. Because bell peppers are an important commercial crop, this organism has undergone a great deal of agricultural research. It is thought that too much water aids the spread of the pathogen. Two fields are under study. The first
In her book Red Ink Behaviors, Jean Hollands reports on the assessment of leading Silicon Valley companies regarding a manager’s lost time due to inappropriate behavior of employees. Consider the following independent random variables. The variable x1 measures manager’s hours per week lost due
This problem is based on information regarding productivity in leading Silicon Valley companies. In large corporations, an “intimidator” is an employee who tries to stop communication, sometimes sabotages others, and, above all, likes to listen to him- or herself talk. Let x1 be a random
Given x1 and x2 distributions that are normal or approximately normal with unknown Ï1 and Ï2, the value of t corresponding to 1 - 2 has a distribution that is approximated by a Students t distribution. We use the convention that the degrees of freedom are
Consider independent random samples from two populations that are normal or approximately normal, or the case in which both sample sizes are at least 30. Then, if Ï1 and Ï2 are unknown but we have reason to believe that Ï1 = Ï2, we can pool the standard
Redo Problem 15(a) using the critical region method, and compare your results to those obtained using the P-value method.Problem 15A random sample of n1 = 10 regions in New England gave the following violent crime rates (per million population):x1: New England crime rateAnother random sample of n2
Redo Problem 11(a) using the critical region method, and compare your results to those obtained using the P-value method. Problem 11 REM (rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both REM and non-REM sleep. However, it is thought that children have
Josh and Kendra each calculated a 90% confidence interval for the difference of means using a Student’s t distribution for random samples of size n1 = 20 and n2 = 31. Kendra followed the convention of using the smaller sample size to compute d.f. = 19. Josh used his calculator and
A random sample of 49 measurements from one population had a sample mean of 10, with sample standard deviation 3. An independent random sample of 64 measurements from a second population had a sample mean of 12, with sample standard deviation 4. Test the claim that the population means are
Two populations have mound-shaped, symmetrical distributions. A random sample of 16 measurements from the first population had a sample mean of 20, with sample standard deviation 2. An independent random sample of 9 measurements from the second population had a sample mean of 19, with sample
A random sample of 49 measurements from a population with population standard deviation 3 had a sample mean of 10. An independent random sample of 64 measurements from a second population with population standard deviation 4 had a sample mean of 12. Test the claim that the population means are
This problem is based on information taken from The Rating Guide to Life in America’s Fifty States, by G. S. Thomas. A random sample of n1 = 288 voters registered in the state of California showed that 141 voted in the last general election. A random sample of n2 = 216 registered voters in the
Based on information from Harper’s Index, r1 = 37 out of a random sample of n1 = 100 adult Americans who did not attend college believe in extraterrestrials. However, out of a random sample of n2 = 100 adult Americans who did attend college, r2 = 47 claim that they believe in extraterrestrials.
Do you prefer paintings in which the people are fully clothed? This question was asked by a professional survey group on behalf of the National Arts Society. A random sample of n1 = 59 people who are conservative voters showed that r1 = 45 said yes. Another random sample of n2 = 62 people who are
Redo Problem 7 using the critical region method, and compare your results to those obtained using the P-value method. Problem 7 Would you favor spending more federal tax money on the arts? This question was asked by a research group on behalf of The National Institute. Of a random sample of n1 =
Redo Problem 8 using the critical region method, and compare your results to those obtained using the P-value method.Problem 8Would you favor spending more federal tax money on the arts? This question was asked by a research group on behalf of The National Institute. Of a random sample of n1 = 93
Consider two independent binomial experiments. In the first one, 40 trials had 10 successes. In the second one, 50 trials had 15 successes. (a) Is it appropriate to use a normal distribution to approximate the 1 - 2 distribution? Explain. (b) Find a 90% confidence interval for p1 - p2. (c) Based
Consider two independent binomial experiments. In the first one, 40 trials had 15 successes. In the second one, 60 trials had 6 successes. (a) Is it appropriate to use a normal distribution to approximate the 1 - 2 distribution? Explain. (b) Find a 95% confidence interval for p1 - p2. (c) Based
Isabel Myers was a pioneer in the study of personality types. She identified four basic personality preferences that are described at length in the book Manual: A Guide to the Development and Use of the Myers-Briggs Type Indicator, by Myers and McCaulley (Consulting Psychologists Press). Marriage
Most married couples have two or three personality preferences in common. Myers used a random sample of 375 married couples and found that 132 had three preferences in common. Another random sample of 571 couples showed that 217 had two personality preferences in common. Let p1 be the population
S. C. Jett is a professor of geography at the University of California, Davis. He and a colleague, V. E. Spencer, are experts on modern Navajo culture and geography. The following information is taken from their book Navajo Architecture: Forms, History, Distributions (University of Arizona Press).
Unknown cultural affiliations and loss of identity at high elevations. These are words used to propose the hypothesis that archaeological sites tend to lose their identity as altitude extremes are reached. This idea is based on the notion that prehistoric people tended not
(a) Suppose that a 95% confidence interval for a difference of proportions contains both positive and negative numbers. Will a 99% confidence interval based on the same data necessarily contain both positive and negative numbers? Explain. What about a 90% confidence interval? Explain. (b) Suppose
In the Focus Problem at the beginning of this chapter, a study was described comparing the hatch ratios of wood-duck nesting boxes. Group I nesting boxes were well separated from each other and well hidden by available brush. There were a total of 474 eggs in group I boxes, of which a field count
For one binomial experiment, 75 binomial trials produced 45 successes. For a second independent binomial experiment, 100 binomial trials produced 70 successes. At the 5% level of significance, test the claim that the probabilities of success for the two binomial experiments differ. (a) Compute the
For one binomial experiment, 200 binomial trials produced 60 successes. For a second independent binomial experiment, 400 binomial trials produced 156 successes. At the 5% level of significance, test the claim that the probability of success for the second binomial experiment is greater than that
Would you favor spending more federal tax money on the arts? This question was asked by a research group on behalf of The National Institute. Of a random sample of n1 = 220 women, r1 = 59 responded yes. Another random sample of n2 = 175 men showed that r2 = 56 responded yes. Does this information
Would you favor spending more federal tax money on the arts? This question was asked by a research group on behalf of The National Institute. Of a random sample of n1 = 93 politically conservative voters, r1 = 21 responded yes. Another random sample of n2 = 83 politically moderate voters showed
Generally speaking, would you say that most people can be trusted? A random sample of n1 = 250 people in Chicago ages 18–25 showed that r1 = 45 said yes. Another random sample of n2 = 280 people in Chicago ages 35–45 showed that r2 = 71 said yes (based on information from the National Opinion
Six sets of identical twins were randomly selected from a population of identical twins. One child was taken at random from each pair to form an experimental group. These children participated in a program designed to promote creative thinking. The other child from each pair was part of the control
The following data represent soil water content (percentage of water by volume) for independent random samples of soil taken from two experimental fields growing bell peppers.Soil water content from field I: x1; n1 = 72Soil water content from field II: x2; n2 = 80 (a) Use a calculator with mean and
How profitable are different sectors of the stock market? One way to answer such a question is to examine profit as a percentage of stockholder equity. A random sample of 32 retail stocks such as Toys “Я” Us, Best Buy, and Gap was studied for x1, profit as a percentage of stockholder equity.
A random sample of 18 adult male wolves from the Canadian Northwest Territories gave an average weight 1 = 98 lb with estimated sample standard deviation s1 = 6.5 lb. Another sample of 24 adult male wolves from Alaska gave an average weight 2 = 90 lb with estimated sample standard deviation s2 =
A random sample of 17 wolf litters in Ontario, Canada, gave an average of 1 = 4.9 wolf pups per litter with estimated sample standard deviation s1 = 1.0. Another random sample of 6 wolf litters in Finland gave an average of 2 = 2.8 wolf pups per litter with sample standard deviation s2 = 1.2. (a)
The book Survey Responses: An Evaluation of Their Validity, by E. J. Wentland and K. Smith (Academic Press), includes studies reporting the accuracy of answers to questions from surveys. A study by Locander and others considered the question “Are you a registered voter?” Accuracy of response
Locander and others also studied the accuracy of responses on questions involving more sensitive material than voter registration. From public records, individuals were identified as having been charged with drunken driving not less than 6 months or more than 12 months from the starting date of the
A marketing consultant was hired to visit a random sample of five sporting goods stores across the state of California. Each store was part of a large franchise of sporting goods stores. The consultant taught the managers of each store better ways to advertise and display their goods. The net sales
The following problem is based on information taken from the pediatrics section of The Merck Manual (a commonly used reference in medical schools and nursing programs). Let x be the body weight of a child (in kilograms), and let y be the metabolic rate of the child (in 100 kcal/24 h).ˆ‘x = 100;
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