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statistics for engineers and scientists

Questions and Answers of Statistics For Engineers And Scientists

9.51 The yield stresses were studied for two sizes of steel rods, with results as follows:Estimate the average increase in yield stress of the 14-mm rod over the 10-mm rod, with a confidence
9.47 The total amount of hydrogen chloride (HCl) in columns above an altitude of 12 kilometers was measured at selected sites over the El Chichon volcano both before and after an eruption. (See
9.41 A measurement of physiological activity important to runners is the rate of oxygen consumption.Research Quarterly, May 1979, reports on the differences between oxygen consumption rates for
8.66 An aircraft subassembly paint shop has the task of painting a variety of reworked aircraft parts.Some parts are large and require hours to paint, whereas some are small and can be painted in a
8.64 Quality control in glass production involves counting the number of defects observed in samples of a fixed size periodically selected from the production process. For 20 samples, the observed
8.62 Woven fabric from a certain loom is controlled for quality by periodically sampling 1-square-meter specimens and counting the number of defects.For 15 such samples, the observed number of
8.61 Bolts being produced in a certain plant are checked for tolerances. Those not meeting tolerance specifications are considered to be defective. Fifty bolts are gauged for tolerance every hour.
8.59 Filled bottles of soft drink coming off a production line are checked for underfilling. One hundred bottles are sampled from each half-day’s production. The results for 20 such samples are
8.58 Bronze castings are controlled for copper content.Ten samples of five specimens each gave the measurements on percentage of copper that are listed in table on the next page.a Construct control
8.54 Production of ammeters is controlled for quality by periodically selecting an ammeter and obtaining four measurements on a test circuit designed to produce 15 amps. The data in table below were
7.49 Let X1 and X2 have a joint distribution that is uniform over the region shaded in the diagram below.a Find the marginal density for X2.b Find the marginal density for X1.c Find P[(X1 X2)
7.3 The same study that produced the seat belt safety data of Table 7.1 also took into account the age of the child involved in a fatal accident. The results for those children wearing no seat belts
20. ADVANCED TOPIC: Participants 1 and 2 are in Group A; participants 3, 4, 5, and 6 are in Group B; and participants 7, 8, and 9 are in Group C. Make a table showing nominal coding for these nine
19. ADVANCED TOPIC: Do the following for the scores in practice problems (a)16, (b) 17, and (c) 18: (i) Figure the analysis of variance using the structural model approach from “Introduction to the
18. ADVANCED TOPIC: For following scores, figure the t test using the.05 level, two-tailed. Then figure a one-way analysis of variance (also .05 level) using the structural model method from
17. ADVANCED TOPIC: For the following scores, figure a t test for independent means (.05 level, two-tailed) and an analysis of variance (.05 level) using the structural model method from
16. ADVANCED TOPIC: For the following scores, carry out a t test for independent means (two-tailed) and an analysis of variance using the structural model method from “Introduction to the Analysis
15. Do the following for the scores in practice problems (a) 16, (b) 17, and (c)18: (i) Figure a t test for independent means, (ii) figure the correlation coefficient(between the group that
14. Group I consists of 12 people whose scores have a mean of 15.5 and a population variance estimate of 4.5. Group B also consists of 12 people:M = 18.3, S2= 3.5. Carry out a t test for independent
13. The following are scores from three data sets. Figure the t tests for these using the .01 level, two-tailed. Then, for each, also figure a one-way analysis of variance(also .01 level) using the
12. Following are three data sets. For the first two data sets, in addition to the means and estimated population variances, we have shown the t test information. You should figure the third
11. (a) Look up and write down the F cutoff at the .01 level for distributions with 1 degree of freedom in the numerator and 10, 20, 30, and 60 degrees of freedom in the denominator. (b) Take the
10. ADVANCED TOPIC: Participants 1, 2, and 3 are in Group I; participants 4 and 5 are in Group II; participants 6, 7, and 8 are in Group III; and participants 9 and 10 are in Group IV. Make a table
9. ADVANCED TOPIC: Do the following for the scores in practice problems (a) 6,(b) 7, and (c) 8: (i) Figure the analysis of variance using the structural model approach from “Introduction to the
8. ADVANCED TOPIC: For the following scores, figure a t test for independent means and then figure an analysis of variance using the structural model approach from “Introduction to the Analysis of
7. ADVANCED TOPIC: For the following scores, figure a t test using the .05 level, two-tailed. Then figure a one-way analysis of variance (also .05 level)using the structural model method from
6. ADVANCED TOPIC: For the following scores, figure a t test for independent means (two-tailed) and then figure an analysis of variance using the structural model approach from “Introduction to the
5. Do the following for the scores in practice problems (a) 6, (b) 7, and (c) 8:(i) Figure a t test for independent means, (ii) figure the correlation coefficient(between the group that participants
4. Group A includes 10 people whose scores have a mean of 170 and a population variance estimate of 48. Group B also includes 10 people: M = 150, S2= 32.Carry out a t test for independent means
3. Following is a data set. Figure the t test for this problem. Then, also figure a one-way analysis of variance using the regular method of “Introduction to the Analysis of Variance” (not the
2. Following are two data sets. For the first data set, in addition to the means and estimated population variances, we have shown the t test information. You should figure the second yourself. Also,
1. (a) Look up and write down the t cutoff at the .05 level (two-tailed) for 5, 10, 15, and 20 degrees of freedom. (b) Square each t cutoff and write it down next to the t. (c) Look up and write
4. (a) What is nominal coding? (b) How is it done? (c) Why is it done? (d) Why can’t you just use a single numeric variable with more than two values? (e) In a particular study, participants 1 and
3. Based on what you have learned in previous sections, give an argument for why, when there are only two groups, the analysis of variance and correlation should give the same significance.
2. When there are only two groups, explain the similarity between the analysis of variance structural model approach and regression in terms of (a) SS Total,(b) SS Within and SS Error, (c) SS Between
1. Under what conditions can you use the analysis of variance to find the significance of a bivariate prediction or correlation?
6. (a) Why do researchers use t tests and analyses of variance when they could use correlation or regression instead? (b) What is an advantage of using regression and correlation over using analysis
5. How do the variables in an analysis of variance correspond to the variables in a regression?
4. When you make a scatter diagram for the scores in a t test for independent means, (a) what does it look like, and (b) where does the regression line go?
3. (a) What is the effect of the scores being spread out around their mean, and(b) why, for the t test for independent means?
2. How can you make a two-level nominal variable that divides the groups into a numeric variable that you can use in correlation or regression?
1. How can you understand a difference between groups on a measured variable in terms of an association between a predictor and a criterion variable?
25. Irving and Berel (2001) compared the effects of four kinds of programs (three actual programs and a control group) designed to make women more skeptical of media portrayals of female body image.
24. Everett and colleagues (1997) mailed a survey to a random sample of physicians.Half were offered $1 if they would return the questionnaire (this was the experimental group); the other half served
23. About how many participants do you need for 80% power in each of the following planned studies, using a chi-square test for independence with p 6 .05?Predicted Effect Size Design(a) Small 2 *
22. What is the power of the following planned studies, using a chi-square test for independence with p 6 .05?Predicted Effect Size Design N(a) Medium 2 * 2 100(b) Medium 2 * 3 100(c) Large 2 * 2
21. Figure the effect size for the following studies:N Chi-Square Design(a) 40 10 2 * 2(b) 400 10 2 * 2(c) 40 10 4 * 4(d) 400 10 4 * 4(e) 40 20 2 * 2
20. A comparative psychologist tests rats, chimpanzees, and humans on a particular learning task. The following table shows the numbers of each species that were and were not able to learn the task.
19. The following results are of a survey of a sample of people buying ballet tickets, laid out according to the type of seat they purchased and how regularly they attend.Is there a significant
18. Carry out a chi-square test for independence for each of the following contingency tables (use the .05 level). Also, figure the effect size for each contingency table.(a) 8 8 (b) 8 8 (c) 8 8 8 16
17. Carry out a chi-square test for independence for each of the following contingency tables (use the .05 level). Also, figure the effect size for each contingency table.(a) 0 18 (b) 0 0 18 18 0 9 9
16. Stasser and colleagues (1989) conducted a study involving discussions of three different “candidates,” which were described to participants in a way the researchers intended to make the
15. A researcher wants to be sure that the sample in her study is not unrepresentative of the distribution of ethnic groups in her community. Her sample includes 300 whites, 80 African Americans, 100
14. Carry out a chi-square test for goodness of fit for each of the following studies(use the .05 level for each). In each situation, the observed numbers are shown;the expected numbers are equal
13. Carry out a chi-square test for goodness of fit for each of the following studies(use the .01 level for each):(a) Category Expected Observed 1 2% 5 2 14% 15 3 34% 90 4 34% 120 5 14% 50 6 2% 20(b)
12. Wilfley and colleagues (2001), in a study of binge eating disorder, compared 37 women getting treatment in a clinic to a control group of 108 otherwise similar women from the general community.
11. Lydon and his associates (1997) conducted a study that compared long-distance to local dating relationships. The researchers first administered questionnaires to a group of students one month
10. About how many participants do you need for 80% power in each of the following planned studies using a chi-square test for independence with p 6 .05?Predicted Effect Size Design(a) Medium 2 *
9. What is the power of the following planned studies using a chi-square test for independence with p 6 .05?Predicted Effect Size Design N(a) Small 2 * 2 25(b) Medium 2 * 2 25(c) Small 2 * 2 50(d)
8. Figure the effect size for the following studies:N Chi-Square Design(a) 100 16 2 * 2(b) 100 16 2 * 5(c) 100 16 3 * 3(d) 100 8 2 * 2(e) 200 16 2 * 2
7. A political psychologist is interested in whether the community a person lives in is related to that person’s opinion on an upcoming water conservation ballot initiative.The psychologist surveys
6. A developmental psychologist is interested in whether children of three different ages (5, 8, and 11 years) differ in their liking for a certain kind of music.The psychologist studies 200 children
5. Carry out a chi-square test for independence for each of the following contingency tables (use the .01 level). Also, figure the effect size for each contingency table.(a) 10 16 (b) 100 106 (c) 100
4. Folwell and others (1997) interviewed a group of adults, aged 54 and older, about their relationships with their siblings. One question they asked was whether there had been a change in emotional
1. Carry out a chi-square test for goodness of fit for each of the following studies(use the .05 level for each):(a) Category Expected Observed A 20% 19 B 20% 11 C 40% 10 D 10% 5 E 10% 5(b) Category
5. Explain how and why the scores from Steps ❸ and ❹ of the hypothesis-testing process are compared. Explain the meaning of the result of this comparison with regard to the specific research and
4. Describe how to figure the chi-square value for the sample. The key idea is to get a single number that indicates the overall discrepancy between what was found in the study and what would be
3. Explain that the comparison distribution in this situation is a chi-square distribution.Be sure to mention that the shape of the chi-square distribution depends on the number of degrees of
2. Describe the core logic of hypothesis testing in this situation. Be sure to mention that the hypothesis testing involves comparing observed frequencies (that is, frequencies found in the actual
1. Explain that chi-square tests are used for hypothesis testing with nominal variables.The chi-square test for goodness of fit is used to test hypotheses about whether a distribution of frequencies
25. Ask five other students of the same gender as yourself (each from different families) to give you their own height and also their mother’s height. Determine the linear prediction rule for
24. Think of something that you would like to be able to predict and what two or more predictor variables would be useful in predicting it. (This should be different from any example given in class
23. Think of something that you would like to be able to predict and what predictor variable would be useful in predicting it. (This should be different from any example given in class or used for a
22. Social psychologists studying criminal justice issues have long been interested in what influences people’s attitudes about punishment of criminal offenders.Graham and her colleagues (1997)
21. Nezlek and colleagues (1997) had participants first write self-descriptions and then exchange them with four other students also taking part in the study. Then the students privately ranked the
20. For each of the following, (a) through (d), determine the multiple linear prediction rule for predicting criterion variable Y from predictor variables X 1, X 2, and X3. Then (e) figure the
19. Repeat problem 18, doing parts (a) through (f), but this time predicting the number of hours of watching violent television from violent acts, and using values of 2, 5, and 7 for parts (c), (d),
18. The results for the amount of violent television watched and the amount of violent behavior toward their playmates for four young children are presented here, including the means.Child’s Code
17. Repeat problem 15, doing parts (a) through (f), but this time adding an additional pair of scores, with a dexterity value of 4 and an value of 10 (this pair of scores can be thought of as an
16. Repeat problem 15, doing parts (a) through (f), but this time predicting dexterity from anxiety, and using values of 0, 4, and 7 for parts (c), (d), and (e), respectively.
15. Four individuals were given a test of manual dexterity (high scores mean better dexterity) and an anxiety test (high scores mean more anxiety). The results are presented here, including the
14. For each of the following, (a) through (d), determine the linear prediction rule for predicting criterion variable Y from predictor variable X. Then (e) make a single graph (with values from 0 to
13. A clinical psychologist has found that scores on a new depression scale predict satisfaction with psychotherapy. The regression constant in the linear prediction rule for predicting satisfaction
12. A personnel psychologist studying adjustment to the job of new employees found that employees’ amount of education (in number of years) predicts ratings by job supervisors two months later. The
11. Mize and Petit (1997) were interested in the impact of a mother’s style of helping her child understand social interactions on the child’s social life. These researchers arranged for 43
10. In the Oettingen and colleagues (2001) study described earlier (in the “Prediction in Research Articles” section), in addition to studying anticipated disappointment, the researchers
9. For each of the following, (a) through (d), determine the multiple linear prediction rule for predicting criterion variable Y from predictor variables X1, X2, and X3. Then (e) figure the predicted
8. Repeat problem 6, doing parts (a) through (f), but this time adding an additional pair of scores, with a therapist empathy value of 95 and a patient satisfaction value of 1 (this pair of scores
7. Repeat problem 6, doing parts (a) through (f), but this time predicting empathy from satisfaction, and using values of 3, 2, and 1 for parts (c), (d), and (e), respectively.
6. A pilot study of the relation between psychotherapists’ degree of empathy and their patients’ satisfaction with therapy studies four patient–therapist pairs. The results are presented here,
5. Repeat problem 4, doing parts (a) through (f), but this time predicting hours studied from test grade, and using values of 70, 75, and 80 for parts (c), (d), and(e), respectively.
4. An instructor asked five students how many hours they had studied for an exam.The number of hours studied and their grades, along with the means, are shown here. (a) Determine the linear
3. For each of the following, (a) through (d), determine the linear prediction rule for predicting criterion variable Y from predictor variable X. Then (e) make a single graph (with values from 0 to
22. Arbitrarily select eight people from your class whose name you know. Do each of the following: (a) Make a scatter diagram for the relation between the number of letters in each person’s first
21. Table 12 is from a study by Baldwin and colleagues (2006) that examined the associations among feelings of shame, guilt, and self-efficacy in a sample of 194 college students. Self-efficacy
20. Gable and Lutz (2000) studied 65 children, 3 to 10 years old, and their parents.One of their results was “Parental control of child eating showed a negative association with children’s
19. As part of a larger study, Speed and Gangstead (1997) collected ratings and nominations on a number of characteristics for 66 fraternity men from their fellow fraternity members. The following
18. About how many participants are needed for 80% power in each of the following planned studies that will use a correlation coefficient and the .05 significance level?Effect Size (r ) Tails(a) .10
17. What is the power of each of the following studies using a correlation coefficient and the .05 significance level?Effect Size (r ) N Tails(a) .10 30 1(b) .30 40 2(c) .50 50 2(d) .30 100 2(e) .10
16. (The instructions for this problem are shown after problem 14.) A developmental psychologist studying people in their eighties was interested in the relation between number of very close friends

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