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elementary statistics
Just The Essentials Of Elementary Statistics 10th Edition Robert Johnson, Patricia Kuby - Solutions
10.165 Design your own study involving two populations.a. Determine a set of questions that compare the means, proportions, or variances of two populations of interest to you. You might consider two different class levels as the two populations and questions similar to the following: Is there is a
10.164 [EX10-001] How do credit card debts for freshmen and sophomores compare? Using the two sets of sample data on page 546:a. Find the proportion of each sample that have at least one credit card.b. Find the point estimate for the difference between the two proportions.c. Are the assumptions for
10.163 [EX10-163] A research project was undertaken to evaluate the amount of force needed to elicit a designated response on equipment made from two distinct designs: the existing design and an improved design. The expectation was that new design equipment would require less force than the current
10.162 [EX10-162] Random samples of counties in North Dakota and South Dakota were selected from the USDA-NASS website for the purpose of estimating the difference between the mean 2001 yield rates for oat production for the two states.Yield, ND 66.0 73.8 51.9 61.3 67.4 54.0 71.4 58.0 56.2 40.0
10.161 Mindy Fernandez is in charge of production at the new sport utility vehicle (SUV) assembly plant that just opened in her town. Lately she has been concerned that the wheel lug bolts do not match the chrome lug nuts close enough to keep the assembly of the wheels operating smoothly.Workers
10.160 A soft-drink distributor is considering two new models of dispensing machines. Both the Harvard Company machine and the Fizzit machine can be adjusted to fill the cups to a certain mean amount. However, the variation in the amount dispensed from cup to cup is a primary concern.Ten cups
10.159 A manufacturer designed an experiment to compare the difference between men and women with respect to the times they require to assemble a product. A total of 15 men and 15 women were tested to determine the time they required, on average, to assemble the product. The time required by the
10.158 “It’s a draw,” according to two Australian researchers. “By age 25, up to 29% of all men and up to 34% of all women have some gray hair, but this difference is so small that it’s considered insignificant.”Source: “Silver Threads Among the Gold: Who’ll Find Them First, a Man
10.157 Who wins disputed cases whenever there is a change made to the tax laws, the taxpayer or the Internal Revenue Service (IRS)? The latest trend indicates that the burden of proof in all court cases has shifted from the taxpayers to the IRS, which tax experts predict could set off more
10.156 A study in the New England Journal of Medicine reported that based on 987 deaths in southern California, right-handers died at an average age of 75 and left-handers died at an average age of 66.In addition, it was found that 7.9% of the lefties died from accident-related injuries, excluding
10.155 According to “Venus vs. Mars” in the May/June 2005 issue of Arthritis Today, men and women may be more alike than we think. The Boomers Wellness Lifestyle Survey of men and women aged 35 to 65 found that 88% of women considered “managing stress” important for maintaining overall
10.154 In determining the “goodness” of a test question, a teacher will often compare the percentage of better students who answer it correctly with the percentage of poorer students who answer it correctly. One expects that the proportion of better students who will answer the question
10.153 A consumer group compared the reliability of two comparable microcomputers from two different manufacturers. The proportion requiring service within the first year after purchase was determined for samples from each of two manufacturers.Manufacturer Sample Size Proportion Needing Service 1
10.152 A survey was conducted to determine the proportion of Democrats as well as Republicans who support a “get tough” policy in South America.The results of the survey were as follows:Democrats: n 250, number in support 120 Republicans: n 200, number in support 105 Construct the 98%
10.151 [EX10-151] At a large university, a mathematics placement exam is administered to all students.This exam has a history of producing scores with a mean of 77. Samples of 36 male students and 30 females students are randomly selected from this year’s student body and the following scores
10.150 [EX10-150] A group of 17 students participated in an evaluation of a special training session that claimed to improve memory. The students were randomly assigned to two groups:group A, the test group, and group B, the control group. All 17 students were tested for the ability to remember
10.149 [EX10-149] The material used in making parts affects not only how long the part lasts but also how difficult it is to repair. The following measurements are for screw torque removal for a specific screw after several operations of use. The first row lists the part number, the second row
10.148 To compare the merits of two short-range rockets, 8 of the first kind and 10 of the second kind are fired at a target. If the first kind has a mean target error of 36 feet and a standard deviation of 15 feet and the second kind has a mean target error of 52 feet and a standard deviation of
10.147 Some 20 million Americans visit chiropractors annually, and the number of practitioners in the United States is 55,000, nearly double the number two decades ago, according to the American Chiropractic Association. The New England Journal of Medicine released a report showing the results of a
10.146 A test concerning some of the fundamental facts about acquired immunodeficiency syndrome(AIDS) was administered to two groups, one consisting of college graduates and the other consisting of high school graduates. A summary of the test results follows:College graduates: n 75, x 77.5, s
10.145 George Johnson is the head coach of a college football team that trains and competes at home on artificial turf. George is concerned that the 40-yard sprint time recorded by his players and others increases substantially when running on natural turf as opposed to artificial turf. If so,
10.144 [EX10-144] Sucrose, ordinary table sugar, is probably the single most abundant pure organic chemical in the world and the one most widely known to nonchemists. Whether from sugar cane(20% by weight) or sugar beets (15% by weight), and whether raw or refined, common sugar is still sucrose.
10.143 [EX10-143] Two methods were used to study the latent heat of ice fusion. Both method A(an electrical method) and method B (a method of mixtures) were conducted with the specimens cooled to 0.72°C. The data in the following table represent the change in total heat from 0.72°C to water at
10.142 [EX10-142] An achievement test in a beginning computer science course was administered to two groups. One group had a previous computer science course in high school; the other group did not. The test results follow. Assuming test scores are normal, construct a 98% confidence interval for
10.141 [EX10-141] Ten soldiers were selected at random from each of two companies to participate in a rifle-shooting competition. Their scores are shown in the following table.Company A 72 29 62 60 68 59 61 73 38 48 Company B 75 43 63 63 61 72 73 82 47 43 Construct a 95% confidence interval for the
10.140 The same achievement test is given to soldiers selected at random from two units. The scores they attained are summarized as follows:Unit 1: n1 70, x1 73.2, s1 6.1 Unit 2: n2 60, x2 70.5, s2 5.5 Construct a 90% confidence interval for the difference in the mean level of the two
10.139 A test that measures math anxiety was given to 50 male and 50 female students. The results were as follows:Males: x 70.5, s 13.2 Females: x 75.7, s 13.6 Construct a 95% confidence interval for the difference between the mean anxiety scores.
10.138 [EX10-138] Immediate-release medications quickly deliver their drug content, with the maximum concentration reached in a short time;sustained-release medications, on the other hand, take longer to reach maximum concentration. As part of a study, immediate-release codeine (irc)was compared
10.137 [EX10-137] The amount of general anesthetic a patient should receive prior to surgery has received considerable public attention. According to the American Society of Anesthesiologists, every year, about 40,000 (some researchers have put the figure closer to 200,000) of the 28 million
10.136 [EX10-136] At the end of their first day at training camp, 10 new recruits participated in a rifle-shooting competition. The same 10 competed again at the end of a full week of training and practice.Their resulting scores are shown in the following table.Recruit Time of Competition 1 2 3 4 5
10.135 [EX10-135] We want to know which of two types of filters should be used. A test was designed in which the strength of a signal could be varied from zero to the point where the operator first detects the image. At this point, the intensity setting is recorded. Lower settings are better.Twenty
10.134 [EX10-134] The diastolic blood pressure readings for 15 patients were determined using two techniques: the standard method used by medical personnel and a method using an electronic device with a digital readout. The results were as follows:Patient 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
10.133 [EX10-133] Using a 95% confidence interval, estimate the mean difference in IQ between the oldest and the youngest members (brothers and sisters) of a family based on the following random sample of IQs. Assume normality.Oldest 145 133 116 128 85 100 105 150 97 110 120 130 Youngest 131 119
10.132 A chemist is testing a newly proposed analytical method and decides to use the currently accepted method for comparison. She takes 12 specimens of unknown concentrate and determines the concentration of each specimen, using both the proposed method and the current method. Do these two
10.131 It was stated in this section that the F-test is very sensitive to minor departures from the assumptions. Repeat Exercise 10.130 using N(100, 20) and N(120, 30). Notice that the only change from Exercise 10.130 is the seemingly slight increase in the standard deviation of the second
10.130 Use a computer to demonstrate the truth of the theory presented in this section.a. The underlying assumptions are “the populations are normally distributed,” and while conducting a hypothesis test for the equality of two standard deviations, it is assumed that the standard deviations are
10.128 [EX10-128] Americans snooze on the weekends, according to a poll of 1506 adults for the National Sleep Foundation and reported in a USA Snapshot during April 2005.Hours of Sleep Weekdays Weekends Less than 6 0.16 0.10 6–6.9 0.24 0.15 7–7.9 0.31 0.24 8 or more 0.26 0.49 Two independent
10.126 [EX10-126] Several counties in Minnesota and Wisconsin were randomly selected, and information about the 2001 sweet corn crop was collected. The following yield rates in tons of sweet corn per acre harvested resulted.Yield, MN 5.90 6.50 6.20 5.90 6.20 5.70 5.91 5.90 6.00 5.60 6.51 6.30
10.125 [EX10-125] The quality of the end product is somewhat determined by the quality of the materials used. Textile mills monitor the tensile strength of the fibers used in weaving their yard goods. The following independent random samples are tensile strengths of cotton fibers from two
10.124 Referring to Applied Example 10.20 (p. 599):a. What null and alternative hypotheses did Carpenter and Raza test?b. What does “p 0.005” mean?c. Use a computer or calculator to calculate the p-value for F(237, 305) 1.36.
10.123 When a hypothesis test is two-tailed and Excel is used to calculate the p-value, what additional step must be taken?
10.122 [EX10-122] A study was conducted to determine whether or not there was equal variability in male and female systolic blood pressure readings.Random samples of 16 men and 13 women were used to test the experimenter’s claim that the variances were unequal. MINITAB was used to calculate the
10.121 Sucrose, ordinary table sugar, is probably the single most abundant pure organic chemical in the world and the one most widely known to nonchemists.Whether from sugar cane (20% by weight) or sugar beets (15% by weight), and whether raw or refined, common sugar is still sucrose. Fifteen U.S.
10.120 A study in Pediatric Emergency Care compared the injury severity between younger and older children. One measure reported was the Injury Severity Score (ISS). The standard deviation of ISS scores for 37 children 8 years or younger was 23.9, and the standard deviation for 36 children older
10.119 A bakery is considering buying one of two gas ovens. The bakery requires that the temperature remain constant during a baking operation. A study was conducted to measure the variance in temperature of the ovens during the baking process. The variance in temperature before the thermostat
10.118a. Two independent samples, each of size 3, are drawn from a normally distributed population. Find the probability that one of the sample variances is at least 19 times larger than the other one.b. Two independent samples, each of size 6, are drawn from a normally distributed population. Find
10.117 What would be the value of F in Example 10.20 if F were used? Why is it less than 1?
10.116 Calculate F given s2 1 3.2 and s2 2 2.6.
10.115 Calculate F given s1 3.2 and s2 2.6.
10.113 Find the critical value for the hypothesis test with Ha: 1 2, with n1 7, n2 10, and 0.05.
10.111 Find the following critical values for F from Tables 9A, 9B, and 9C in Appendix B.a. F (24, 12, 0.05)b. F (30, 40, 0.01)c. F (12, 10, 0.05)d. F (5, 20, 0.01)e. F (15, 18, 0.025)f. F (15, 9, 0.025)g. F (40, 30, 0.05) h. F (8, 40, 0.01)
10.110 Find the values of F(12, 24, 0.01) and F(24, 12, 0.01).
10.108 Express the Ho and Ha of Example 10.18(p. 598) equivalently in terms of standard deviations.
10.106 State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test the following claims:a. The standard deviation of population X is smaller than the standard deviation of population Y.b. The ratio of the variances of population A over population B is greater than
10.105 State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test the following claims:a. The variances of populations A and B are not equal.b. The standard deviation of population I is larger than the standard deviation of population II.c. The ratio of the
10.104 The guidelines to ensure the sampling distribution of p1 p2 is normal include several conditions about the size of several values. The two binomial distributions B(100, 0.3) and B(100, 0.4)satisfy all of those guidelines.a. Verify that B(100, 0.3) and B(100, 0.4) satisfy all guidelines.b.
10.103 A 2005 Harris Interactive for Korbel poll found that 63% of men and 55% of women think that it is okay for women to make marriage proposals to men. An 8% difference may or may not be statistically significant. What size sample is required to make this difference significant?Source: USA
10.102 Adverse side effects are always a concern when testing and trying new medicines. Placebocontrolled clinical studies were conducted in patients 12 years of age and older who were receiving“once-a-day” doses of Allegra, a seasonal allergy drug. The following results were published in the
10.101 Forty-one small lots of experimental product were manufactured and tested for the occurrence of a particular indication that is attribute in nature yet causes rejection of the part. Thirty-one lots were made using one particular processing method, and ten lots were made using yet a second
10.100 Both parents and students have many concerns when considering colleges. One of the top three concerns according to the Fall 2004 College Partnership study is “Choosing best major/career.”Nineteen percent of the parents reported “Choosing best major/career” as a major concern, whereas
10.99 The Committee of 200, a professional organization of preeminent women entrepreneurs and corporate leaders, reported the following: 60%of women MBA students say “businesses pay their executives too much money” and 50% of the men MBA students agreed.a. Does there appear to be a difference
10.98 In a survey of families in which both parents work, one of the questions asked was, “Have you refused a job, promotion, or transfer because it would mean less time with your family?” A total of 200 men and 200 women were asked this question.“Yes” was the response given by 29% of the
10.97 Two randomly selected groups of citizens were exposed to different media campaigns that dealt with the image of a political candidate. One week later, the citizen groups were surveyed to see whether they would vote for the candidate. The results were as follows:Exposed to Exposed to
10.96 PC users are often victimized by hardware problems. A study revealed that hardware problems reported to manufacturers could not be fixed by one in three owners of personal computers.Home PC owners fared even worse than those with work PCs, facing longer waits for service and getting even
10.93 Find the p-value for the test with alternative hypothesis pE pR using the data in Exercise 10.91.
10.92 Find the value of z that would be used to test the difference between the proportions, given the following:Sample n x G 380 323 H 420 332
10.91 Find the values of p p and q p for these samples:Sample x n E 15 250 R 25 275
10.89 State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test these claims:a. There is no difference between the proportions of men and women who will vote for the incumbent in next month’s election.b. The percentage of boys who cut classes is greater than
10.88 In a survey of 300 people from city A, 128 preferred New Spring soap to all other brands of deodorant soap. In city B, 149 of 400 people preferred New Spring soap. Find the 98% confidence interval for the difference in the proportions of people from the two cities who prefer New Spring soap.
10.87 The proportions of defective parts produced by two machines were compared, and the following data were collected:Machine 1: n 150; number of defective parts 12 Machine 2: n 150: number of defective parts 6 Determine a 90% confidence interval for p1 p2.
10.86 In a random sample of 40 brown-haired individuals, 22 indicated that they used hair coloring.In another random sample of 40 blonde individuals, 26 indicated that they used hair coloring.Use a 92% confidence interval to estimate the difference in the population proportions of brunettes and
10.85 “The game’s appeal for teenagers ‘is the same as for adults’,” an article in USA Today (December 21, 2004), reported on a poll of 200 male and 199 female teenagers aged 14 to 17. The findings reported were that 66% of the male teenagers have “ever gambled” and 37% of the female
10.84 Find the 95% confidence interval for pA pB.Sample n x A 125 45 B 150 48
10.83 A Nursing Economics article titled “Nurse Executive Turnover” compared two groups of nurse executives. One group had participated in a unique program for nurse executives called the Wharton Fellows Program, and the other group had not participated in the program. Of 341 Wharton Fellows,
10.82 Calculate the maximum error of estimate for a 90% confidence interval for the difference between two proportions for the following cases:a. n1 40, p1 0.7, n2 44, and p2 0.75b. n1 36, p1 0.33, n2 38, and p2 0.42
10.81 Calculate the estimate for the standard error of the difference between two proportions for each of the following cases:a. n1 40, p1 0.8, n2 50, and p2 0.8b. n1 33, p1 0.6, n2 38, and p2 0.65
10.80 If n1 40, p1 0.9, n2 50, and p2 0.9:a. Find the estimated values for both np’s and both nq’s.b. Would this situation satisfy the guidelines for approximately normal? Explain.
10.79 Only 75 of the 250 people interviewed were able to name the vice president of the United States. Find the values for x, n, p , and q .
10.78 One assumption for the two-sample t-test is the “sampled populations are to be normally distributed.”What happens when they are not normally distributed? Repeat Exercise 10.75 using two theoretical populations that are not normal and using samples of size 10. The exponential distribution
10.77 Unbalanced sample sizes is a factor in determining the number of degrees of freedom for inferences about the difference between two means.Repeat Exercise 10.75 using theoretical normal distributions of N(100, 20) and N(120, 20) and sample sizes of 5 and 20. Check all three properties of the
10.76 One reason for being conservative when determining the number of degrees of freedom to use with the t-distribution is the possibility that the population variances might be unequal. Extremely different values cause a lowering in the number of df used. Repeat Exercise 10.75 using theoretical
10.75 Use a computer to demonstrate the truth of the statement describing the sampling distribution of x1 x2. Use two theoretical normal populations:N1(100, 20) and N2(120, 20).a. To get acquainted with the two theoretical populations, randomly select a very large sample from each. Generate
10.74 [EX10-074] When evaluating different measuring instruments, one must first determine whether there is a systematic difference between the instruments. Lenses from two different groups(1 and 2) were measured once each by two different instruments. The measurement differences(Instrument A
10.73 [EX10-073] Penfield and Perinton are two adjacent eastside suburbs of Rochester, New York.In previous years, they have always been considered on equal ground with respect to quality of life, housing, and education. Many new housing developments are currently going up in Penfield, and it
10.72 [EX10-072] Many people who are involved with major league baseball (MLB) believe that games played by the New York Yankees tend to last longer than games played by other teams. To test this theory, one other MLB team was picked at random, namely, the St. Louis Cardinals. The time of game
10.71 [EX10-071] Twenty laboratory mice were randomly divided into two groups of 10. Each group was fed according to a prescribed diet. At the end of 3 weeks, the weight gained by each animal was recorded. Do the data in the following table justify the conclusion that the mean weight gained on diet
10.70 [EX10-070] According to the College Board(http://www.collegeboard.com/press/article/0,3,8993,00.html), the average 2004–2005 cost (tuition, fees, and room and board) for a public college is$11,354 versus $26,057 for a private college. Is there also a difference in the average cost of
10.69 [EX10-069] MINITAB was used to complete a t-test of the difference between the two means using the following two independent samples.Sample 1 33.7 21.6 32.1 38.2 33.2 35.9 34.1 39.8 23.5 21.2 23.3 18.9 30.3 Sample 2 28.0 59.9 22.3 43.3 43.6 24.1 6.9 14.1 30.2 3.1 13.9 19.7 16.6 13.8 62.1 28.1
10.68 A study was conducted to assess the safety and efficiency of receiving nitroglycerin from a transdermal system (i.e., a patch worn on the skin), which intermittently delivers the medication, versus taking oral medication (pills). Twenty patients who suffer from angina (chest pain) due to
10.67 Referring to Applied Example 10.11:a. The “Variances Unequal” is equivalent to making no assumption about the variances.Verify the value reported for the estimated standard error, SE of Difference.b. Verify the t-value.c. What is the range of possible values for df for this study?d.
10.66 One could reason that high school seniors would seem to have more money issues than high school juniors. Seniors foresee expenses for college as well as their senior trip and prom. So does this mean that they work more than their junior classmates?Christine, a senior at HFL High School,
10.65 Lauren, a brunette, was tired of hearing“blondes have more fun.” She set out to “prove”that “brunettes are more intelligent.” Lauren randomly(as best she could) selected 40 blondes and 40 brunettes at her high school. The following overall grade statistics were calculated:Blondes
10.64 The purchasing department for a regional supermarket chain is considering two sources from which to purchase 10-lb bags of potatoes. A random sample taken from each source shows the following results.Idaho Supers Idaho Best Number of Bags Weighed 100 100 Mean Weight 10.2 lb 10.4 lb Sample
10.63 The computer age has allowed teachers to use electronic tutorials to motivate their students to learn. Issues in Accounting Education published the results of a study that showed that an electronic tutorial, along with intentionally induced peer pressure, was effective in enhancing preclass
10.62 If a random sample of 18 homes south of Center Street in Provo has a mean selling price of$145,200 and a standard deviation of $4700, and a random sample of 18 homes north of Center Street has a mean selling price of $148,600 and a standard deviation of $5800, can you conclude that there is a
10.61 Many cheeses are produced in the shape of a wheel. Because of the differences in consistency between these different types of cheese, the amount of cheese, measured by weight, varies from wheel to wheel. Heidi Cembert wishes to determine whether there is a significant difference, at the 10%
10.60 “In a typical month, men spend $178 and women spend $96 on leisure activities,” according to the results of an International Communications Research (ICR) for American Express poll, as reported in USA Snapshot found on the Internet June 25, 2005.Suppose random samples are taken from the
10.59 Suppose the calculated t had been 1.80 in Example 10.10 (pp. 569–570). Using df 9 or using df 20 results in different answers. Explain how the word conservative (p. 565) applies here.
10.58 For the hypothesis test involving Ha: B A 0 with df 18 and t 1.3.a. Find the p-value.b. Find the critical values given 0.05.
10.57 Determine the critical values that would be used for the following hypothesis tests (using the classical approach) about the difference between two means with population variances unknown.a. Ha: 1 2 0, n1 26, n2 16, 0.05b. Ha: 1 2 0, n1 36, n2 27, 0.01c. Ha: 1
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