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mathematics
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Introduction To Probability And Statistics 14th Edition William Mendenhall, Robert Beaver, Barbara Beaver - Solutions
Use Table 5 in Appendix I to bound the p-value for a chi-square test: a. X2 = 4.29, df = 5 b. X2 = 20.62, df = 6
Does a baby's sleeping position affect the development of motor skills? In one study, 343 full-term infants were examined at their 4-month checkup for various developmental milestones, such as rolling over, grasping a rattle, and reaching for an object.14 The baby's predominant sleep
Refer to Exercise 14.40. Find the p-value for the large-sample z-test in part a. Compare this p-value with the p-value for the chi-square test, shown in the partial MINITAB printout.Partial MINITAB output for Exercise 14.41Chi-Square Test: Prone, SideChi-Sq = 9.795, DF = 1, P-Value = 0.002Exercise
The researchers in Exercise 14.40 also measured several other developmental milestones and their relationship to the infant's predominant sleep position.14 The results of their research are presented in the table for the 320 infants at their 4-month checkup.Use your knowledge of the analysis of
A botanist performs a secondary cross of petunias involving independent factors that control leaf shape and flower color, where the factor A represents red color, a represents white color, B represents round leaves, and b represents long leaves. According to the Mendelian model, the plants should
A CBS News Poll15 asked the question "Compared to your parents' generation, do you think in general your opportunities to succeed in life are better than theirs, about the same as theirs, or worse than theirs?" on three separate dates over a 10-year period. All surveys involved n = 1048
A study to determine the effectiveness of a drug (serum) for arthritis resulted in the comparison of two groups, each consisting of 200 arthritic patients. One group was inoculated with the serum; the other received a placebo (an inoculation that appears to contain serum but actually is non
A survey was conducted to determine student, faculty, and administration attitudes about a new university parking policy. The distribution of those favoring or opposing the policy is shown in the table. Do the data provide sufficient evidence to indicate that attitudes about the parking policy are
The chi-square test used in Exercise 14.45 is equivalent to the two-tailed z-test of Section 9.6 provided a is the same for the two tests. Show algebraically that the chi-square test statistic X2 is the square of the test statistic z for the equivalent test.
You can use a goodness-of-fit test to determine whether all of the criteria for a binomial experiment have actually been met in a given application. Suppose that an experiment consisting of four trials was repeated 100 times. The number of repetitions on which a given number of successes was
Infections sometimes occur when blood transfusions are given during surgical operations. An experiment was conducted to determine whether the injection of antibodies reduced the probability of infection. An examination of the records of 138 patients produced the data shown in the table. Do the data
Suppose that a response can fall into one of k 5 categories with probabilities p1, p2, . . . , p5 and that n = 300 responses produced these category counts:a. Are the five categories equally likely to occur? How would you test this hypothesis? b. If you were to test this hypothesis using the chi
U.S. labor unions have traditionally been content to leave the management of the company to managers and corporate executives. But in Europe, worker participation in management decision making is an accepted idea that is continually spreading. To study the effect of worker participation in
An occupant-traffic study was conducted to aid in the remodeling of an office building that contains three entrances. The choice of entrance was recorded for a sample of 200 persons who entered the building. Do the data in the table indicate that there is a difference in preference for the three
Graduate students' responsibilities are often related to their roles as teaching assistants or research assistants. As part of a larger study, K.M. McGoldrick and her colleagues investigated the level of preparation of economics graduate students for their teaching- related duties for students at
How confident are you that the food you purchase is safe to eat? This question was asked in a CBS News Poll:17 the data that follow reflect the results of the responses to this poll.a. Is there sufficient evidence to conclude that there are significant differences in responses between men and women
Each model year seems to introduce new colors and different hues for a wide array of vehicles, from luxury cars, to full-size or intermediate models, to compacts and sports cars, to light trucks. However, white and silver/gray continue to make the top five or six colors across all of these
Refer to Exercise 14.54. The researcher wants to see if there is a difference in the color distributions for compact/sports cars versus full/intermediate cars.18Another random sample of 250 full/intermediate cars was taken and the color of the vehicles was recorded. The table below shows the
Pfizer Canada Inc. is a pharmaceutical company that makes azithromycin, an antibiotic in a cherry-flavored suspension used to treat bacterial infections in children. To compare the taste of their product with three competing medications, Pfizer tested 50 healthy children and 20 healthy adults.
The prevalence and patterns of knee injuries among women collegiate rugby players were investigated using a sample questionnaire, to which 42 rugby clubs responded.20 A total of 76 knee injuries were classified by type as well as the position (forward or back) of the player.Chi-Square Test: Men
Is a customer's preference for a fast-food chain affected by the age of the customer? If so, advertising might need to target a particular age group. Suppose a random sample of 500 fast-food customers aged 16 and older was selected, and their favorite fast-food restaurants along with their age
Is your chance of getting a cold influenced by the number of social contacts you have? A study by Sheldon Cohen, a psychology professor at Carnegie Mellon University, seems toshow that the more social relationships you have, the less susceptible you are to colds.21 A group of 276 healthy men and
Suppose that a response can fall into one of k = 3 categories with probabilities p1 = .4, p2 = .3, and p3 = .3, and n = 300 responses produce these category counts:Do the data provide sufficient evidence to indicate that the cell probabilities are different from those specified for the three
A criminologist studying criminal offenders who have a record of one or more arrests is interested in knowing whether the educational achievement level of the offender influences the frequency of arrests. He has classified his data using four educational level classifications:A: completed 6th grade
A department store manager claims that her store has twice as many customers on Fridays and Saturdays than on any other day of the week (the store is closed on Sundays). That is, the probability that a customer visits the store Friday is 2/8, the probability that a customer visits the store
A freeway with four lanes in each direction was studied to see whether drivers prefer to drive on the inside lanes. A total of 1000 automobiles were observed during heavy earl morning traffic, and the number of cars in each lane was recorded:Do the data present sufficient evidence to indicate that
A peony plant with red petals was crossed with another plant having streaky petals. Ageneticist states that 75% of the offspring from this cross will have red flowers. To test this claim, 100 seeds from this cross were collected and germinated, and 58 plants had red petals. Use the chi-square
Researchers from Germany have concluded that the risk of a heart attack for a working person may be as much as 50% greater on Monday than on any other day.1 The researchers kept track of heart attacks and coronary arrests over a period of 5 years among 330,000 people who lived near Augsburg,
How have the roles of working women changed in America? How many of the jobs in America are held by women? How has advertising refocused their ads to influence the 31% of women who are the primary breadwinners in their family? The latest numbers put women's share of the 130.2 million jobs in
Suppose you want to use the Wilcoxon rank sum test to detect a shift in distribution 1 to the right of distribution 2 based on samples of size n1 = 6 and n2 = 8.a. Should you use T1 or T*1 as the test statistic?b. What is the rejection region for the test if α = .05?c. What is the rejection region
How does Aaron Rodgers, quarterback for the 2011 Super Bowl winners, the Minnesota Vikings, compare to Drew Brees, quarterback for the 2010 Super Bowl winners, the New Orleans Saints? The table below shows the number of completed passes for each athlete during the 2010 NFL football season:3Use the
The weights of turtles caught in two different lakes were measured to compare the effects of the two lake environments on turtle growth. All the turtles were the same age and were tagged before being released into the lakes. The weights for n1 = 10 tagged turtles caught in lake 1 and n2 = 8 caught
Cancer treatment by means of chemicals-chemotherapy-kills both cancerous and normal cells. In some instances, the toxicity of the cancer drug-that is, its effect on normal cells-can be reduced by the simultaneous injection of a second drug. A study was conducted to determine whether a particular
Suppose you wish to use the sign test to test Ha : p > .5 for a paired-difference experiment with n = 25 pairs. a. State the practical situation that dictates the alternative hypothesis given. b. Use Table 1 in Appendix I to find values of a (a < .15) available for the test.
Repeat the instruction of Exercise 15.13 for Ha : p≠.5. Exercise 15.13 Suppose you wish to use the sign test to test Ha : p > .5 for a paired-difference experiment with n = 25 pairs. a. State the practical situation that dictates the alternative hypothesis given. b. Use Table 1 in Appendix I to
Repeat the instructions of Exercises 15.13 and 15.14 for n = 10, 15, and 20. Exercise 15.13 Suppose you wish to use the sign test to test Ha : p > .5 for a paired-difference experiment with n = 25 pairs. State the practical situation that dictates the alternative hypothesis given. Use Table 1 in
A paired-difference experiment was conducted to compare two populations. The data are shown in the table. Use a sign test to determine whether the population distributions are different.a. State the null and alternative hypotheses for the test. b. Determine an appropriate rejection region with
In Exercise 10.46, you compared the property evaluations of two tax assessors, A and B. Their assessments for eight properties are shown in the table:a. Use the sign test to determine whether the data present sufficient evidence to indicate that one of the assessors tends to be consistently more
Two gourmets, A and B, rated 22 meals on a scale of 1-10. The data are shown in the table. Do the data provide sufficient evidence to indicate that one of the gourmets tends to give higher ratings than the other? Test by using the sign test with a value of a near .05.a. Use the binomial tables in
A study reported in the American Journal of Public Health (Science News)-the first to follow blood lead levels in law abiding handgun hobbyists using indoor firing ranges-documents a significant risk of lead poisoning. 4 Lead exposure measurements were made on 17 members of a law enforcement
Refer to Exercise 15.1. Suppose the alternative hypothesis is that distribution 1 is shifted either to the left or to the right of distribution 2. a. Should you use T1 or T*1 as the test statistic? b. What is the rejection region for the test if α = .05? c. What is the rejection region for the
Clinical data concerning the effectiveness of two drugs in treating a particular disease were collected from 10 hospitals. The numbers of patients treated with the drugs varied from one hospital to another. You want to know whether the data present sufficient evidence to indicate a higher recovery
Suppose you wish to detect a difference in the locations of two population distributions based on a paired-difference experiment consisting of n = 30 pairs. a. Give the null and alternative hypotheses for the Wilcoxon signed-rank test. b. Give the test statistic. c. Give the rejection region for
Refer to Exercise 15.21. Suppose you wish to detect only a shift in distribution 1 to the right of distribution 2. a. Give the null and alternative hypotheses for the Wilcoxon signed-rank test. b. Give the test statistic. c. Give the rejection region for the test for α = .05. d. If T+ = 249, what
Refer to Exercise 15.21. Conduct the test using the large-sample z-test. Compare your results with the nonparametric test results in Exercise 15.22, part d. Exercise 15.21 Suppose you wish to detect a difference in the locations of two population distributions based on a paired-difference
Refer to Exercise 15.22. Conduct the test using the large-sample z-test. Compare your results with the nonparametric test results in Exercise 15.21, part d. Exercise 15.22 Refer to Exercise 15.21. Suppose you wish to detect only a shift in distribution 1 to the right of distribution 2. a. Give the
Refer to Exercise 15.16 and data set EX1516. The data in this table are from a paired-difference experiment with n = 7 pairs of observations.a. Use Wilcoxon's signed-rank test to determine whether there is a significant difference between the two populations. b. Compare the results of part a with
In Exercise 15.17, you used the sign test to determine whether the data provided sufficient evidence to indicate a difference in the distributions of property assessments for assessors A and B. a. Use the Wilcoxon signed-rank test for a paired experiment to test the null hypothesis that there is no
The number of machine breakdowns per month was recorded for 9 months on two identical machines, A and B, used to make wire rope:a. Do the data provide sufficient evidence to indicate a difference in the monthly breakdown rates for the two machines? Test by using a value of a near .05. b. Can you
Refer to the comparison of gourmet meal ratings in Exercise 15.18, and use the Wilcoxon signed-rank test to determine whether the data provide sufficient evidence to indicate a difference in the ratings of the two gourmets. Test by using a value of a near .05. Compare the results of this test with
Two methods for controlling traffic, A and B, were used at each of n 12 intersections for a period of 1 week, and the numbers of accidents that occurred during this time period were recorded. The order of use (which method would be employed for the first week) was selected in a random manner. You
Observations from two random and independent samples, drawn from populations 1 and 2, are given here. Use the Wilcoxon rank sum test to determine whether population 1 is shifted to the left of population 2.a. State the null and alternative hypotheses to be tested. b. Rank the combined sample from
Eight people were asked to perform a simple puzzle-assembly task under normal conditions and under stressful conditions. During the stressful time, a stimulus was delivered to subjects 3 minutes after the start of the experiment and every 30 seconds thereafter until the task was completed. Blood
A psychology class performed an experiment to determine whether a recall score in which instructions to form images of 25 words were given differs from an initial recall score for which no imagery instructions were given. Twenty students participated in the experiment with the results listed in the
Three treatments were compared using a completely randomized design. The data are shown in the table.Do the data provide sufficient evidence to indicate a difference in location for at least two of the population distributions? Test using the Kruskal-Wallis H statistic with α = .05.
Four treatments were compared using a completely randomized design. The data are shown here:Do the data provide sufficient evidence to indicate a difference in location for at least two of the population distributions? Test using the Kruskal-Wallis H statistic with α = .05.
Exercise 11.13 presents data on the rates of growth of vegetation at four swampy underdeveloped sites. Six plants were randomly selected at each of the four sites to be used in the comparison. The data are the mean leaf length per plant (in centimeters) for a random sample of 10 leaves per plant.a.
Exercise 11.60 presented data (data set EX1160) on the heart rates for samples of 10 men randomly selected from each of four age groups. Each man walked a treadmill at a fixed grade for a period of 12 minutes, and the increase in heart rate (the difference before and after exercise) was recorded
A sampling of the acidity of rain for 10 randomly selected rainfalls was recorded at three different locations in the United States: the Northeast, the Middle Atlantic region, and the Southeast. The pH readings for these 30 rainfalls are shown in the table.a. Do the data present sufficient evidence
The results of an experiment to investigate product recognition for three advertising campaigns were reported in Example 11.14. The responses were the percentage of 400 adults who were familiar with the newly advertised product. The normal probability plot indicated that the data were not
A randomized block design is used to compare three treatments in six blocks.a. Use the Friedman Fr-test to detect differences in location among the three treatment distributions. Test using a .05. b. Find the approximate p-value for the test in part a. c. Perform an analysis of variance and give
A randomized block design is used to compare four treatments in eight blocks.a. Use the Friedman Fr-test to detect differences in location among the four treatment distributions. Test using α =.05. b. Find the approximate p-value for the test in part a. c. Perform an analysis of
Independent random samples of size n1 = 20 and n2 = 25 are drawn from non normal populations 1 and 2. The combined sample is ranked and T1 = 252. Use the large-sample approximation to the Wilcoxon rank sum test to determine whether there is a difference in the two population distributions.
In Exercise 11.43 (and data set EX1143), we compared the regular prices at four different grocery stores for eight items purchased on the same day. The prices are listed in the table.a. Does the distribution of the prices differ from one supermarket to another? Test using the Friedman Fr-test with
An experiment was conducted to compare the effects of three toxic chemicals, A, B, and C, on the skin of rats. One-inch squares of skin were treated with the chemicals and then scored from 0 to 10 depending on the degree of irritation. Three adjacent 1-inch squares were marked on the backs of eight
In a study of the palatability of antibiotics in children, Dr. Doreen Matsui and colleagues used a voluntary sample of healthy children to assess their reactions to the taste of four antibiotics.5 The children's response was measured on a 10-centimeter (cm) visual analog scale incorporating the use
Give the rejection region for a test to detect positive rank correlation if the number of pairs of ranks is 16 and you have these a-values: a. α = .05 b. α = .01
Give the rejection region for a test to detect negative rank correlation if the number of pairs of ranks is 12 and you have these a-values: a. α = .05 b. α = .01
Give the rejection region for a test to detect rank correlation if the number of pairs of ranks is 25 and you have these a-values: a. α = .05 b. α = .01
The following paired observations were obtained on two variables x and y:a. Calculate Spearman's rank correlation coefficient rs. b. Do the data present sufficient evidence to indicate a correlation between x and y? Test using α =.05.
A political scientist wished to examine the relationship between the voter image of a conservative political candidate and the distance (in miles) between the residences of the voter and the candidate. Each of 12 voters rated the candidate on a scale of 1-20.a. Calculate Spearman's rank correlation
Is the number of years of competitive running experience related to a runner's distance running performance? The data on nine runners, obtained from the study by Scott Powers and colleagues, are shown in the table:6a. Calculate the rank correlation coefficient between years of competitive running x
The data shown in the accompanying table give measures of bending stiffness and twisting stiffness as determined by engineering tests on 12 tennis racquets.a. Calculate the rank correlation coefficient rs between bending stiffness and twisting stiffness. b. If a racquet has bending stiffness, is it
Suppose you wish to detect a shift in distribution 1 to the right of distribution 2 based on sample sizes n1 = 12 and n2 = 14. If T1 = 193, what do you conclude? Use α = .05.
A school principal suspected that a teacher's attitude toward a first-graderdepended on his original judgment of the child's ability. The principal also suspected that much of that judgment was based on the first-grader's IQ score, which was usually known to the teacher. After three weeks of
Refer to Exercise 15.50. Do the data provide sufficient evidence to indicate a positive correlation between the teacher's ranks and the ranks of the IQs? Use α = .05.Exercise 15.50A school principal suspected that a teacher's attitude toward a first-grader depended on his original
Two art critics each ranked 10 paintings by contemporary (but anonymous) artists in accordance with their appeal to the respective critics. The ratings are shown in the table. Do the critics seem to agree on their ratings of contemporary art? That is, do the data provide sufficient evidence to
An experiment was conducted to study the relationship between the ratings of a tobacco leaf grader and the moisture content of the tobacco leaves. Twelve leaves were rated by the grader on a scale of 1-10, and corresponding readings of moisture content were made.Calculate rs. Do the data provide
A social skills training program was implemented with seven mildly challenged students in a study to determine whether the program caused improvements in pre/post measures and behavior ratings. For one such test, the pre- and posttest scores for the seven students aregiven in the table:a. Use a
An experiment was conducted to compare the response times for two different stimuli. To remove natural person-to person variability in the responses, both stimuli were presented to each of nine subjects, thus permitting an analysis of the differences between stimuli within each person. The table
Refer to Exercise 15.55. Test the hypothesis that no difference exists in the distributions of response times for the two stimuli, using the Wilcoxon signed-rank test. Use a rejection region for which a is as near as possible to the a achieved in Exercise 15.55, part a.Excecise 15.55An experiment
To compare two junior high schools, A and B, in academic effectiveness, an experiment was designed requiring the use of 10 sets of identical twins, each twin having just completed the sixth grade. In each case, the twins in the same set had obtained their schooling in the same classrooms at each
Refer to Exercise 15.57. What answers are obtained if Wilcoxon's signed-rank test is used in analyzing the data? Compare with your earlier answers.Exercise 15.57.To compare two junior high schools, A and B, in academic effectiveness, an experiment was designed requiring the use of 10 sets of
The coded values for a measure of brightness in paper (light reflectivity), prepared by two different processes, are given in the table for samples of nine observations drawn randomly from each of the two processes. Do the data present sufficient evidence to indicate a difference in the brightness
In some tests of healthy, elderly men, a new drug has restored their memory almost to that of young people. It will soon be tested on patients with Alzheimer's disease, the fatal brain disorder that destroys the mind. According to Dr. Gary Lynch of the University of California, Irvine, the drug,
Assume (as in the case of measurements produced by two well-calibrated measuring instruments) the means of two populations are equal. Use the Wilcoxon rank sum statistic for testing hypotheses concerning the population variances as follows:a. Rank the combined sample.b. Number the ranked
An experiment was conducted to compare the tenderness of meat cuts treated with two different meat tenderizers, A and B. To reduce the effect of extraneous variables, the data were paired by the specific meat cut, by applying the tenderizers to two cuts taken from the same steer, by cooking paired
A large corporation selects college graduates for employment using both interviews and a psychological achievement test. Interviews conducted at the home office of the company are far more expensive than the tests that can be conducted on campus. Consequently, the personnel office was interested in
Refer to Exercise 15.62. Do the data present sufficient evidence to indicate that the correlation between interview rankings and test scores is less than zero? If this evidence does exist, can you say that tests can be used to reduce the number of interviews?Exercise 15.62A large corporation
A comparison of reaction times for two different stimuli in a psychological word-association experiment produced the accompanying results when applied to a random sampleof 16 people:Do the data present sufficient evidence to indicate a difference in mean reaction times for the two stimuli? Use an
The table gives the scores of a group of 15 students in mathematics and art. Use Wilcoxon's signed-rank test to determine whether the median scores for these students differ significantly for the two subjects.
Refer to Exercise 15.65. Compute Spearman's rank correlation coefficient for these data and test H0 : no association between the rank pairs at the 10% level of significance.Exercise 15.65The table gives the scores of a group of 15 students in mathematics and art. Use Wilcoxon's signed-rank test to
Exercise 11.68 presented an analysis of variance of the yields of five different varieties of wheat, observed on one plot each at each of six different locations (see data set EX1168). The data from this randomized block design are listed here:a. Use the appropriate nonparametric test to determine
In Exercise 11.61, you compared the numbers of sales per trainee after completion of one of four different sales training programs (see data set EX1161). Six trainees completed training program 1, eight completed program 2, and so on. The numbers of sales per trainee are shown in the table.a. Do
In Exercise 11.66, you performed an analysis of variance to compare the mean levels of effluents in water at four different industrial plants (see data set EX1166). Five samples of liquid waste were taken at the output of each of four industrial plants. The data are shown in the tablea. Do the data
Refer to Exercise 15.6. Suppose that two more groups of 10 men each are tested on the number of nonsense syllables they can remember after 5 minutes. However, this time the 65-70-year-olds are given a mild dose of ampakine CX-516. Do the data provide sufficient evidence to conclude that this drug
Scientists have shown that a newly developed vaccine can shield rhesus monkeys from infection by a virus closely related to the AIDScausing human immunodeficiency virus (HIV). In their work, Ronald C. Resrosiers and his colleagues at the New England Regional Primate Research Center gave each of n =
An experiment was performed to determine whether there is an accumulation of heavy metals in plants that were grown in soils amended with sludge and whether there is an accumulation of heavy metals in insects feeding on those plants.8 The data in the table are cadmium concentrations (in g/kg) in
Refer to Exercise 15.71. The data in this table are the cadmium concentrations found in aphids that fed on the plants grown in soil amended with sludge.a. Use the diagnostic plots to assess whether the assumptions of normality and constant variance are reasonable in this case.b. Based on your
Before filling several new teaching positions at the high school, the principal formed a review board consisting of five teachers who were asked to interview the 12 applicants and rank them in order of merit. Seven of the 12 applicants held college degrees but had limited teaching experience. Of
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