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statistics principles and methods
Statistics The Exploration And Analysis Of Data 6th Edition John M Scheb, Jay Devore, Roxy Peck - Solutions
=+c. Is your answer to Part (b) consistent with what would be expected for a statistic that has a t distribution? Explain.
=+b. How does the histogram of the t values compare to the z histogram? Be sure to comment on center, shape, and spread.
=+a. Write a brief description of the shape, center and spread for the histogram of the z values. Is what you see in the histogram consistent with what you would have expected to see? Explain. (Hint: In theory, what is the distribution of the z statistic?)
=+■ Are the conclusions drawn consistent with the results of the hypothesis test?
=+■ What is the P-value associated with the test? Was a significance level selected for the test (as opposed to simply reporting the P-value)? Is the chosen significance level reasonable?
=+■ Was the appropriate test used? Does the validity of the test depend on any assumptions about the population from which the sample was selected? If so, are the assumptions reasonable?
=+■ What hypotheses are being tested? Are the hypotheses about a population mean, a population proportion, or some other population characteristic?
=+g. Is the way in which b changes as n,a, s, and m vary consistent with your intuition? Explain.
=+will be based on a sample of n bearings. The diameter distribution is believed to be normal. Determine the value of b in each of the following cases:a. n 5 15, a 5 .05, s 5 0.02, m 5 0.52b. n 5 15, a 5 .05, s 5 0.02, m 5 0.48c. n 5 15, a 5 .01, s 5 0.02, m 5 0.52d. n 5 15, a 5 .05, s 5 0.02, m 5
=+b. What happens to b in each of the cases in Part (a) if s is actually larger than 10? Explain your reasoning.10.71 Let m denote the true average diameter for bearings of a certain type. A test of H0: m 5 0.5 versus Ha: m Þ 0.5
=+a. Assuming s 5 10 and n 5 10, use Appendix Table 5 to findb, the probability of a Type II error, for each of the given alternative values of m when a level .05 test is employed:i. 52 ii. 55 iii. 60 iv. 70
=+10.70 Optical fibers are used in telecommunications to transmit light. Current technology allows production of fibers that transmit light about 50 km (Research at Rensselaer, 1984). Researchers are trying to develop a new type of glass fiber that will increase this distance. In evaluating a
=+c. What is the approximate power of the test when m 5.04 and a 5 .05?
=+what is the approximate value ofb, the probability of a Type II error, when m 5 .04?
=+b. Using s 5 0.0125, a 5 .05, and Appendix Table 5,
=+a. Assuming that the distribution of shaft wear is normal, test at level .05 the hypotheses H0: m 5 .035 versus Ha:m . .035.
=+10.69 The amount of shaft wear after a fixed mileage was determined for each of 7 randomly selected internal combustion engines, resulting in a mean of 0.0372 in. and a standard deviation of 0.0125 in.z 5 x 2 10 0.1 sx 5 0.1.
=+b. What is the power of the test when p 5 .8 and a 5 .05?
=+a. If 102 of the 125 sampled apartments exclude renters with children, would a level .05 test lead you to the conclusion that more than 75% of all apartments exclude children?
=+10.68 The city council in a large city has become concerned about the trend toward exclusion of renters with children in apartments within the city. The housing coordinator has decided to select a random sample of 125 apartments and determine for each whether children are permitted. Let p be
=+d. What is the power of the test when m 5 9.8? when m 5 9.5?
=+c. Without doing any calculation, explain how b when m 5 9.5 compares to b when m 5 9.8. Then check your assertion by computing b when m 5 9.5.
=+b. If the test procedure of Part (a) is used, calculate b when m 5 9.8, and interpret this error probability.
=+a. What is a for the test procedure that rejects H0 if z #21.28?
=+a sample of size 36. Suppose that s is known to be 0.6, from which The appropriate test statistic is then
=+10.67 ▼ Let m denote the true average lifetime for a certain type of pen under controlled laboratory conditions.A test of H0: m 5 10 versus Ha: m , 10 will be based on
=+g. If H0 is rejected when z $ 1.8 and 5 152.8, what is the appropriate conclusion? What type of error might have been made in reaching this conclusion?
=+f. For the hypotheses and test procedure described, what is the value of b if m 5 160?
=+e. For the hypotheses and test procedure described, compute the value of b when m 5 153.
=+d. Suppose that the true value for m is 153 and that H0 is to be rejected if z $ 1.8. Draw a sketch (similar to that of Figure 10.5) of the sampling distribution of , and shade the region that would representb, the probability of making a Type II error.
=+c. The rejection of H0 when z $ 1.8 corresponds to what value of a? (That is, what is the area under the z curve to the right of 1.8?)
=+b. Describe Type I and Type II errors in this context.
=+a. Explain why use of the z statistic is appropriate in this setting.
=+10.66 Water samples are taken from water used for cooling as it is being discharged from a power plant into a river. It has been determined that as long as the mean temperature of the discharged water is at most 1508F, there will be no negative effects on the river ecosystem. To investigate
=+Suppose that it is known that the true average uptake for cultures without nitrates is 8000. Do the data suggest that the addition of nitrates results in a decrease in the true average uptake? Test the appropriate hypotheses using a significance level of .10.10.65 and tha. Exp powerb. Exp the
=+10.64 ● Much concern has been expressed in recent years regarding the practice of using nitrates as meat preservatives. In one study involving possible effects of these chemicals, bacteria cultures were grown in a medium containing nitrates. The rate of uptake of radio-labeled amino acid was
=+a. Is it reasonable to test hypotheses about true average st?240. Does the boxplot t differs from the statede hypotheses suggested in Part (b).
=+a boxplot and normal probability plot:255 244 239 242 265 245 259 248 225 226 251 233
=+10.63 ● ▼ Many consumers pay careful attention to stated nutritional contents on packaged foods when making purchases. It is therefore important that the information on packages be accurate. A random sample of n 5 12 frozen dinners of a certain type was selected from production during a
=+10.62 An article titled “Teen Boys Forget Whatever It Was(Apr form time pend not given in the article, suppose that this mean was based on a random sample of 50 teenage Australian boys and that the sample standard deviation was 1.4 min. Is there convincing evidence that the average attention
=+Suppose that it is reasonable to regard the sample as a random sample from the population of healthy males, age 18–30. Do the data suggest that the population mean MWOL exceeds 25? Carry out a test of the relevant hypotheses using a .05 significance level.
=+10.61 ● ▼ A well-designed and safe workplace can contribute greatly to increasing productivity. It is especially important that workers not be asked to perform tasks, such as lifting, that exceed their capabilities. The following data on maximum weight of lift (MWOL, in kilograms) for a
=+for the population of all males having English as their native language is 10.0 (suggested by data in the article).Does it appear that the population mean for males from non-English-speaking Asian countries is smaller than 10.0?
=+student rarely speaks). For a random sample of 64 males from Asian countries where English is not the official language, the sample mean and sample standard deviation were 8.75 and 2.57, respectively. Suppose that the mean
=+possible values from 3 to 15 (a low value means that a
=+10.60 Typically, only very brave students are willing to speak out in a college classroom. Student participation may be especially difficult if the individual is from a different culture or country. The article “An Assessment of Class Participation by International Graduate Students”(Journal
=+the authors of this paper claiming that the pain reduction attributable to listening to music is not statistically significant, not practically significant, or neither statistically nor practically significant? Explain.
=+10.59 The paper titled “Music for Pain Relief” (The Cochrane Database of Systematic Reviews, April 19, 2006) concluded, based on a review of 51 studies of the effect of music on pain intensity, that “Listening to music reduces pain intensity levels . . . However, the magnitude of these
=+b. Write a few sentences commenting on the results of the test in Part (a) and of the test in Part (b) of the previous exercise.
=+a. Do the sample data provide convincing evidence that the mean number of hours that parents think their teens spend online is less than 10 hours per week?
=+10.58 The same survey referenced in the previous exercise reported that for a random sample of 676 parents of Canadian teens, the mean number of hours parents thought their teens spent online was 6.5 and the sample standard deviation was 8.6.
=+b. Do the sample data provide convincing evidence that the mean number of hours that teens spend online is greater than 10 hours per week?
=+a. What does the large standard deviation, 11.6 hours, tell you about the distribution of online times for this sample of teens?
=+10.57 A survey of teenagers and parents in Canada conducted by the polling organization Ipsos (“Untangling the Web: The Facts About Kids and the Internet,” January 25, 2006) included questions about Internet use. It was reported that for a sample of 534 randomly selected teens, the mean
=+c. Explain why the null hypothesis was rejected in the test of Part (b) but not in the test of Part (a).
=+b. Now suppose that the sample standard deviation was 2 hours. Carry out a hypothesis test with a significance level of .05 to decide if there is convincing evidence that the mean time spent using the Internet by Canadians is greater than 12.5 hours.
=+a. The sample standard deviation was not reported, but suppose that it was 5 hours. Carry out a hypothesis test with a significance level of .05 to decide if there is convincing evidence that the mean time spent using the Internet by Canadians is greater than 12.5 hours.
=+10.56 In a study of computer use, 1000 randomly selected Canadian Internet users were asked how much time they spend using the Internet in a typical week (Ipsos Reid, August 9, 2005). The mean of the 1000 resulting observations was 12.7 hours.
=+long hours in child care and the overall mean for thirdgraders could be small but the researchers could still reach the conclusion that the mean for the child care group is significantly higher than the overall mean for third-graders.
=+10.55 A comprehensive study conducted by the National Institute of Child Health and Human Development tracked more than 1000 children from an early age through elementary school (New York Times, November 1, 2005).The study concluded that children who spent more than 30 hours a week in child care
=+$9.15 and $7.60 respectively. (These values are consistent with a histogram of the sample data that appears in the report.) Do these data provide convincing evidence that the mean minimum purchase amount for which Canadians consider the use of a debit card to be appropriate is less than $10?
=+10.54 The international polling organization Ipsos reported data from a survey of 2000 randomly selected Canadians who carry debit cards (Canadian Account Habits Survey, July 24, 2006). Participants in this survey were asked what they considered the minimum purchase amount for which it would be
=+paper “Comparative Study of Two Computer Mouse Designs” (Cornell Human Factors Laboratory Technical Report RP7992) are given. Use these data to test the hypothesis that the mean wrist extension for people using this new mouse design is greater than 20 degrees. Are any assumptions required
=+10.53 ● Medical research has shown that repeated wrist extension beyond 20 degrees increases the risk of wrist and hand injuries. Each of 24 students at Cornell University used a proposed new mouse design, and while using the mouse their wrist extension was recorded for each one. Data
=+10.52 A credit bureau analysis of undergraduate students credit records found that the average number of credit cards in an undergraduate’s wallet was 4.09 (“Undergraduate Students and Credit Cards in 2004,” Nellie Mae, May 2005). It was also reported that in a random sample of 132
=+c. If t 5 0.47, what conclusion is appropriate?10.51 The true average diameter of ball bearings of a certain type is supposed to be 0.5 in. What conclusion is appropriate when testing H0: m 5 0.5 versus Ha: m Þ 0.5 in each of the following situations:a. n 5 13, t 5 1.6, a 5 .05b. n 5 13, t 5
=+b. If t 5 21.83 and a 5 .01 is selected, what conclusion is appropriate?
=+a. If t 5 22.3 and a 5 .05 is selected, what conclusion is appropriate?
=+the use of a writing machine) is at least 10 hr. A random sample of 18 pens is selected, the writing lifetime of each is determined, and a normal probability plot of the resulting data support the use of a one-sample t test. The relevant hypotheses are H0: m 5 10 versus Ha: m , 10.
=+10.50 A certain pen has been designed so that true average writing lifetime under controlled conditions (involving x 5 5.21
=+: m . 20 based on a sample of 15 observations gave t 5 3.2. What conclusion is appropriate at each of the following significance levels?a. a 5 .05c. a 5 .001b. a 5 .01
=+10.49 Paint used to paint lines on roads must reflect enough light to be clearly visible at night. Let m denote the true average reflectometer reading for a new type of paint under consideration. A test of H0: m 5 20 versus Ha
=+a. Two-tailed test, df 5 9, t 5 0.73b. Upper-tailed test, df 5 10, t 5 20.5c. Lower-tailed test, n 5 20, t 5 22.1d. Lower-tailed test, n 5 20, t 5 25.1e. Two-tailed test, n 5 40, t 5 1.7
=+10.47 Give as much information as you can about the P-value of a t test in each of the following situations:a. Upper-tailed test, df 5 8, t 5 2.0b. Upper-tailed test, n 5 14, t 5 3.2c. Lower-tailed test, df 5 10, t 5 22.4d. Lower-tailed test, n 5 22, t 5 24.2e. T t il d t t df 15 t 1 6f. T g. T
=+10.46 The desired percentage of silicon dioxide in a certain type of cement is 5.0%. A random sample of n 5 36 specimens gave a sample average percentage of .Let m be the true average percentage of silicon dioxide in this type of cement, and suppose that s is known to be 0.38. Test H0: m 5 5
=+10.45 Newly purchased automobile tires of a certain type are supposed to be filled to a pressure of 30 psi. Let m denote the true average pressure. Find the P-value associated with each of the following given z statistic values for testing H0: m 5 30 versus Ha: m Þ 30 when s is known:a. 2.10d.
=+10.44 The article “Fewer Parolees Land Back Behind Bars” (Associated Press, April 11, 2006) includes the following statement: “Just over 38 percent of all felons who were released from prison in 2003 landed back behind bars by the end of the following year, the lowest rate since 1979.”
=+a 5 .01. Would your conclusion be different if a significance level of .05 had been used? Explain.
=+2002). Should the students interpret this result as convincing evidence that the proportion of the time the coin would land heads up is not .5? Test the relevant hypotheses using
=+10.43 Students at the Akademia Podlaka conducted an experiment to determine whether the Belgium-minted Euro coin was equally likely to land heads up or tails up. Coins were spun on a smooth surface, and in 250 spins, 140 landed with the heads side up (New Scientist, January 4,
=+on examining records from 500 randomly selected accidents. Does the study provide convincing evidence that the proportion of accidents involving teenage drivers differs from .07, the proportion of teens in the driving population?
=+10.42 Teenagers (age 15 to 20) make up 7% of the driving population. The article “More States Demand Teens Pass Rigorous Driving Tests” (San Luis Obispo Tribune, January 27, 2000) described a study of auto accidents conducted by the Insurance Institute for Highway Safety. The Institute
=+Suppose that this result was based on a sample of 512 religion surfers. Is there convincing evidence that the proportion of religion surfers who belong to a religious community is different from .68, the proportion for the general population? Use a 5 .05.
=+10.41 ▼ The article “Americans Seek Spiritual Guidance on Web” (San Luis Obispo Tribune, October 12, 2002)reported that 68% of the general population belong to a religious community. In a survey on Internet use, 84% of“religion surfers” (defined as those who seek spiritual help online
=+Census Bureau will keep information confidential? Use a significance level of .01.
=+information you give about yourself is kept confidential.Is there convincing evidence that, despite the advertising
=+10.40 The success of the U.S. census depends on people filling out and returning census forms. Despite extensive advertising, many Americans are skeptical about claims that the Census Bureau will guard the information it collects from other government agencies. In a USA Today poll (March 13,
=+10.39 ▼ In a national survey of 2013 adults, 1590 responded that lack of respect and courtesy in American society is a serious problem, and 1283 indicated that they believe that rudeness is a more serious problem than in past years (Associated Press, April 3, 2002). Is there convincing
=+a hypothesis test to determine if there is convincing evidence to support the claim that fewer than half of adult Americans can name at least one justice currently serving on the Supreme Court.
=+10.38 In a representative sample of 1000 adult Americans, only 430 could name at least one justice who is currently serving on the U.S. Supreme Court (Ipsos, January 10, 2006). Using a significance level of .01, carry out
=+b. Is there sufficient evidence to conclude that a majority of U.S. businesses monitor employees’ web site visits?Test the appropriate hypotheses using a significance level of .01.
=+a. Is there sufficient evidence to conclude that more than 75% of U.S. businesses monitor employees’ web site visits? Test the appropriate hypotheses using a significance level of .01.
=+10.36 The report “2005 Electronic Monitoring & Surveillance Survey: Many Companies Monitoring, Recording, Videotaping—and Firing—Employees” (American Management Association, 2005) summarized the results of a survey of 526 U.S. businesses. Four hundred of these companies indicated that
=+c. Write a few sentences explaining why different conclusions were reached in the hypothesis tests of Parts (a)and (b).
=+b. Suppose that the sample size had been 100 instead of 1000, and that 47 thought that the movie quality was getting worse (so that the sample proportion is still .47).Based on this sample of 100, is there convincing evidence that fewer than half of adult Americans believe that movie quality is
=+a. Is there convincing evidence that fewer than half of adult Americans believe that movie quality is getting worse? Use a significance level of .05.
=+10.35 The article referenced in Exercise 10.34 also reported that 470 of 1000 randomly selected adult Americans thought that the quality of movies being produced was getting worse.
=+the sample can be regarded as a random sample of adult Americans. Is there convincing evidence that more than 20% of adult Americans believe that playing the lottery is the best strategy for accumulating $200,000 in net wealth?
=+10.33 According to a survey of 1000 adult Americans conducted by Opinion Research Corporation, 210 of those surveyed said playing the lottery would be the most practical way for them to accumulate $200,000 in net wealth in their lifetime (“One in Five Believe Path to Riches Is the Lottery,”
=+Agency collected records of personal telephone calls they had made. Is there sufficient evidence to conclude that a majority of U.S. adults feel this way? Test the appropriate hypotheses using a .01 significance level.
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