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applied statistics and probability for engineers
Applied Statistics For Engineers And Scientists 3rd Edition Jay L. Devore, Nicholas R. Farnum, Jimmy A. Doi - Solutions
=+65. Let x denote the IQ of a child randomly selected from a certain large geographical region. Suppose x is known to have (approximately) a normal distribution with 5 15. A parent group wishes to test the hypothesis H0: 5 100 versus Ha: . 100, hoping to reject the null hypothesis and be
=+Use a chi-squared test based on eight classes to test the appropriate hypotheses at a significance level of .05.171 338 238 37 92 287 203 320 88 36 131 32 61 250 99 138 155 183 201 312 89 158 206 170 204 46 323 289 141 319 242 179 249 185 277 95 46 197 251 196 326 124 350 112 37 104 290 47 310 86
=+64. It is hypothesized that when homing pigeons are disoriented in a certain manner, they will exhibit no preference for any direction of flight after takeoff (the direction x, a continuous variable, should be uniformly distributed on the interval from 0°to 360°, so f(x) 5 1y360 on this
=+an estimate of . The expected frequencies for various categories (class intervals) can then be calculated. Use the accompanying data along with x 5 13.086 to decide whether the truncated exponential distribution is a plausible model (x0 5 70 here).Class: 02,8 82,16 162,24 Frequency: 20 8 7
=+hypothesized (“Some Studies on Tuft Weight Distributions in the Opening Room,” Textile Res. J., 1976: 567–573). The mean value of this distribution is 5 (1y ) 2 (x0e 2 x0)y(1 2 e 2 x0). Replacing by x and by n and solving for the latter quantity gives
=+63. In an investigation into the distribution of output tuft weight x of cotton fibers when the input weight was x0, a truncated exponential distribution, f(x) 5 ( e 2 x)y(1 2 e 2 x0) for 0 , x , x0, was
=+Exchanges in 5-Bromodeoxyuridine-Substituted Chromosomes,” Genetics, 1979: 1251–1264). A Poisson model was hypothesized for the distribution of the number of exchanges. Test the fit of such a model to the accompanying data by first estimating and then combining the frequencies for x 5 8 and
=+62. In a genetics experiment, investigators examined 300 chromosomes of a particular type and counted the number of sister-chromatid exchanges on each one (“On the Nature of Sister-Chromatid
=+b. Note that there is one unusually high conductivity reading. Suppose the researchers discovered there was a recording error for this observation. Remove it and repeat part (a). How does the removal of the observation affect the test for normality?
=+a. Employ software to perform a test for normality (such as the Ryan-Joiner test) using a significance level of .05.
=+61. The article cited in Exercise 88 of Chapter 7 gave the following observations on conductivity(% IACS) for eight wire electrodes used for wire electrical-discharge machining:31 28 26 24 33 65 29 29
=+60. The data in Exercise 40 is paired, so a paired t analysis is appropriate if it is plausible that the values of the differences were selected from a normal distribution. Based on the accompanying plot from Minitab, does this appear to be the case?
=+specimens of internally cured concrete that have been set for 28 days:38.7 40.1 40.3 47.5 48.0 56.0 61.1 Minitab gives r 5 .953 as the value of the correlation coefficient test statistic and reported that P-value ..10. Would you use the one-sample t test to test hypotheses about the value of the
=+59. The article from which the data in Exercise 44 of Chapter 7 was obtained also gave the following data on the compressive strength (in MPa) for 7
=+58. The article cited in Exercise 31 of Section 8.2 gave the following observations on bending rigidity ( N ? m) for medium-quality fabric specimens, from which the accompanying Minitab output was obtained:24.6 12.7 14.4 30.6 16.1 9.5 31.5 17.2 46.9 68.3 30.8 116.7 39.5 73.8 80.6 20.3 25.8 30.9
=+b. For each of the situations in part (a), state whether the null hypothesis would be rejected when using a significance level of .05.
=+a. Give as much information as possible for the P-value in each of the following situations:i. n 5 10, r 5 .95 ii. n 5 10, r 5 .90 iii. n 5 25, r 5 .983 iv. n 5 25, r 5 .915
=+57. Consider the Ryan–Joiner test for population normality.
=+ Suppose the employees of a particular company can be classified into one of two groups (1 and 2). There are 14 members in group 1 and 17 in group 2. Eight members of group 1 and three members of group 2 earn salaries greater than the company median salary. Use Fisher’s exact test at
=+Compliance Manual describes the standards and suggested steps for investigating a charge of compensation discrimination. In the statistical analysis section, Fisher’s exact test is recommended as the test of choice. The following is based on the example found in the EEOC Compliance Manual.
=+56. For many years, federal equal employment opportunity laws have prohibited compensation discrimination. However, according to the U.S. Equal Employment Opportunity Commission (EEOC), pay disparities continue to exist in various demographic groups. According to the EEOC website (visited on
=+b. Use Fisher’s exact test to analyze this data and report the P-value based on a two-sided alternative (as did the authors of the cited article). If your software does not perform this test, there are many online calculators that will report the P-value based on this test. One such site is
=+a. Suppose we are interested in testing whether surgery method affects the provision of ondansetron prescriptions. Determine the estimated expected counts based on the chi-squared test method. Do all expected counts exceed 5?
=+TT. To compare differences in postoperative nausea, researchers kept track of the number of prescriptions of ondansetron (a drug to treat nausea and vomiting) that were issued to the TE and TT children. Four out of 34 TE children compared to none of the 53 TT children received such
=+shown it to be less invasive and to have lower risk of postoperative complications.The article “Differences in Pain and Nausea in Children Operated on by Tonsillectomy or Tonsillotomy—a Prospective Follow-Up Study”(J. of Advanced Nursing, 2012) examined the differences in postoperative
=+worldwide. However, because of the invasive nature of the surgery, TE patients often experience severe postoperative complications. Tonsillotomy (TT), an alternative procedure to surgically removing the tonsils, has become increasingly popular because studies have
=+55. Children often suffer from a condition known as tonsillitis in which the tonsils become sore or swollen.When the condition becomes chronic, many sufferers have their tonsils surgically removed by the tonsillectomy (TE) procedure. TE is one of the most common surgeries performed in children
=+54. The article cited in Exercise 53 classified each member of the sample of workers with respect to both gender and level of work-related psychological demands. The following table is consistent with summary results reported in the article:Gender Men Women Low 1692 1324 Job Demand Medium 1838
=+ This study was based on a representative sample (5405 men, 3987 women) of the Quebec working population. The following cross-classification table for this sample on gender versus level of neck pain is consistent with data reported in the article:Gender Men Women Never 3048 1842 Pain
=+or sexual harassment in the workplace. (Advanced statistical techniques were used to show that neck pain was significantly associated with intimidation at work among both male and female workers.)
=+law enforcement officers, dockworkers). Clearly, a dangerous job can lead to illness or death. But can the psychological stress of a work environment affect employees’ overall health? This issue was investigated in the article “Are There Health Effects of Harassment in the Workplace? A
=+53. We often think that occupational hazards are primarily experienced by those who work under dangerous conditions (e.g., construction workers,
=+b. State and test the appropriate hypotheses using 5 .05.
=+a. Does this situation call for a test of homogeneity or a test of independence?
=+52. A random sample of individuals who drive to work in a large metropolitan area was obtained, and each individual was categorized with respect to both size of vehicle and commuting distance (in miles). Does the accompanying data suggest that there is an association between type of vehicle and
=+a potential side effect of the treatment was erectile dysfunction. The other subgroup of size 52 was given the same treatment without counseling. The percentage of the no-counseling subgroup that reported one or more sexual side effects was 15.3%, whereas 43.6% of the counseling subgroup
=+for patients informed of possible side effects to actually experience those side effects. The article cited a study reported in The Journal of Sexual Medicine in which a group of patients diagnosed with benign prostatic hyperplasia was randomly divided into two subgroups. One subgroup of size 55
=+51. A placebo—that is, a fake medication or treatment—is well known to sometimes have a positive effect just because patients often expect the medication or treatment to be helpful. The article “Beware the Nocebo Effect” (The New York Times, Aug. 12, 2012) gave examples of a less
=+b. Carry out a test of hypotheses to decide whether there is an association between the two factors.
=+a. Calculate the proportion of males in each age category; do the same for females. Based on these proportions, does it appear there might be an association between gender and the age when an individual first smokes?
=+50. A random sample of smokers was obtained, and each individual was classified by both gender and age when he or she first started smoking. The data in the accompanying table is consistent with summary results reported in the article “Cigarette Tar Yields in Relation to Mortality in the
=+3. Rating differs by two medals [(G,B), (B,G)].The observed frequencies for these three categories were 69, 102, and 45, respectively. On the hypothesis of equally likely expert ratings and consumer ratings being assigned completely by chance, each of the 9 medal pairs has probability 1y9. Carry
=+2. Rating differs by one medal [(G,S), (S,G), (S,B),(B,S)].
=+1. Rating is the same [(G,G), (B,B), (S,S)].
=+49. The article “The Gap Between Wine Expert Ratings and Consumer Preferences” (Intl. J. of Wine Business Res., 2008: 335–351) studied differences between expert and consumer ratings by considering medal ratings for wines: gold (G), silver (S), or bronze (B). Three categories were then
=+48. An information retrieval system has ten storage locations. Information has been stored with the exUnless otherwise noted, all content on this page is © Cengage Learning.pectation that the long-run proportion of requests for location i is given by i 5 (5.5 2 i 2 5.5 )y30. A sample of 200
=+Does the data suggest that the proportions in commercials are different from the census proportions?Carry out a test of appropriate hypotheses using a significance level of .01.
=+ The 2000 census proportions for these four ethnic groups are .177, .032, .734, and .057, respectively.
=+47. The article “Racial Stereotypes in Children’s Television Commercials” (J. of Adver. Res., 2008: 80–93)reported the following frequencies with which ethnic characters appeared in recorded commercials that aired on Philadelphia television stations.Ethnicity:African American Asian
=+46. Criminologists have long debated whether there is a relationship between weather and violent crime.The author of the article “Is There a Season for Homicide?” (Criminology, 1988: 287–296) classified 1361 homicides according to season, resulting in the accompanying data. Does this data
=+the course for agriculture students. A random sample of n 5 120 clients revealed 52, 38, 21, and 9 from the four courses. Does this data suggest that the percentages on which staffing was based are not correct? State and test the relevant hypotheses using 5 .05.
=+45. A statistics department at a large university maintains a tutoring service for students in its introductory service courses. The service has been staffed with the expectation that 40% of its clients would be from the business statistics course, 30% from engineering statistics, 20% from the
=+44. Say as much as you can about the P-value for a chisquared test in each of the following situations:a. X2 5 7.5, df 5 2b. X2 5 13.0, df 5 6c. X2 5 18.0, df 5 9d. X2 5 21.3, df 5 4e. X2 5 5.0, df 5 3
=+ Carry out a test of hypotheses to decide whether the true average % difference from that stated differs from zero. (Note: The article stated “Although formal statistical methods do not apply to convenience samples, standard statistical tests were employed to summarize the data for exploratory
=+43. The article “The Accuracy of Stated Energy Contents of Reduced-Energy, Commercially Prepared Foods” (J. of the Amer. Dietetic Assoc., 2010: 116–123) presented the accompanying data on vendorstated gross energy and measured value (both in kcal)for 10 different supermarket convenience
=+Does it appear that true average decrease in body fat is more than 2 kg larger for the experimental condition than for the control condition? Carry out a test of appropriate hypotheses using a significance level of .01.
=+they should take measures to lose weight. After 4 months, the sample mean decrease in body fat for the 17 individuals in the experimental group was 6.2 kg with a sample standard deviation of 4.5 kg, whereas the sample mean and standard deviation for the 17 people in the control group were 1.7 kg
=+42. The article “Supervised Exercise Versus NonSupervised Exercise for Reducing Weight in Obese Adults” (J. Sport. Med. Phys. Fit., 2009:85–90) reported on an investigation in which participants were randomly assigned either to a supervised exercise program or a control group.Those in the
=+expenditure [kcal/kg(subject)/lb(clay)]:Worker: 1 2 3 4 5 6 7 Conventional: .0011 .0014 .0018 .0022 .0010 .0016 .0028 Perforated: .0011 .0010 .0019 .0013 .0011 .0017 .0024 Worker: 8 9 10 11 12 13 Conventional: .0020 .0015 .0014 .0023 .0017 .0020 Perforated: .0020 .0013 .0013 .0017 .0015 .0013
=+41. Shoveling is not exactly a high-tech activity but will continue to be a required task even in our information age. The article “A Shovel with a Perforated Blade Reduces Energy Expenditure Required for Digging Wet Clay” (Human Factors, 2010: 492–502)reported on an experiment in which
=+ State and test the appropriate hypotheses. Does the conclusion depend on whether a significance level of .05, .01, or .001 is used?
=+ Does the true average content measured by one method appear to differ from that measured by the other method?
=+40. The article “Selection of a Method to Determine Residual Chlorine in Sewage Effluents” (Water and Sewage Works, 1971: 360–364) reported the results of an experiment in which two different methods of determining chlorine content were used on samples of Cl2-demand-free water for various
=+who were exposed to a more rigorous type of intervention, the article reported that intervention was beneficial for both MSD and RULA scores.)
=+c. From parts (a) and (b) you should have found that for one score the intervention had a significant impact but not for the other score.Keeping in mind what the scores measure, can you offer an explanation of why this may have occurred? (For a group of computer workers
=+b. Assuming that the difference in RULA scores(After–Before) is approximately normal, carry out a test at significance level .05 to decide whether true average difference in RULA scores is different from zero.
=+a. Assuming that the difference in MSD scores(After–Before) is approximately normal, carry out a test at significance level .05 to decide whether true average difference in MSD scores is different from zero.
=+painful body parts reported by the individual. The RULA score is a rating of the individual’s posture, with lower numbers indicating better posture. Each score was determined both before and after the oral presentation intervention. (The textbook author who found this article did find that his
=+optimal positions of the back, shoulders, elbows, and wrists.Both an MSD score and a rapid upper limb assessment (RULA) score were obtained for each participant. The MSD score is the total number of
=+the intervention was in the form of a short oral presentation on how to sit; the preferred heights of chairs, tables, keyboards, and screens; and
=+Musculoskeletal Disorders Among Computer Operators: Comparison Between Ergonomics Interventions at the Workplace” (Ergonomics, 2012: 15711–1585) investigated the impact of a workplace intervention for reducing MSDs for computer workers. For one group of workers
=+39. Parents often urge their children to “sit up straight” when dining to practice good table manners. Although proper posture is part of maintaining good etiquette, research has shown that it can also help in reducing musculoskeletal disorders (MSDs). The authors of “Reducing
=+ Does DES exposure appear to be associated with reduced spatial ability? State and test the appropriate hypotheses using 5 .05. Does the conclusion change if 5 .01 is used?
=+spatial ability test:exposed mean 5 12.6 unexposed mean 5 13.8 standard error of difference 5 sd 1n 5 .5
=+cervical cancer. The article “Effects of Prenatal Exposure to Diethylstilbestrol (DES) on Hemispheric Laterality and Spatial Ability in Human Males” (Hormones and Behavior, 1992: 62–75) discussed a study in which ten males exposed to DES and their unexposed brothers underwent various
=+38. The drug diethylstilbestrol was used for years by women as a nonsteroidal treatment for pregnancy maintenance, but it was banned in 1971 when research indicated a link with the incidence of
=+c. Use the pooled t test to reach a conclusion in Exercise 35.
=+b. Use the pooled t test to test the relevant hypotheses based on the SAS output given in Exercise 33.
=+a. Describe how this variable can be used to form a test statistic and test procedure, the pooled t test, for testing H0: 1 2 2 5 D.
=+37. Exercise 54 in Chapter 7 presented a t variable appropriate for making inferences about 1 2 2 when both population distributions are normal and, in addition, it can be assumed that 1 5 2.
=+b. Carry out a test of hypotheses to decide whether the true average difference in elapsed times differs from zero.
=+a. What if any assumptions are needed before the t inferential procedure can be used to compare true average elapsed times?
=+former product is significantly more expensive than the latter. These products were chosen because they are similar with respect to allocated shelf space and number of alternative brands.Product Sample Size Sample Mean Sample SD Fabric softener 15 30.47 19.15 Washing-up liquid 19 26.53 15.37
=+36. Which factors are relevant to the time a consumer spends looking at a product on the shelf prior to selection? The article “Effects of Base Price Upon Search Behavior of Consumers in a Supermarket”(J. Econ. Psychol., 2003: 637–652) reported the following data on elapsed time (sec) for
=+ Does it appear that true average HAZ depth is larger for the high current condition than for the nonhigh current condition? Carry out a test of appropriate hypotheses using a significance level of .01.
=+ The article reported the impact of various SAW process settings (including current, voltage, and welding speed) on characteristics of the weldment profile. In one investigation, the SAW process was run on various current settings (A) and the depth (mm) of the HAZ was recorded. The data below
=+SAW weldment profile; research has shown that its shape could be related to plate melting efficiency.Authors of the article wanted to investigate how certain settings of the welding process affect macrostructure zones of the SAW weldment profile. The heat affected zone (HAZ), a band created
=+pipes. During welding, the SAW electrode causes a slight deformation on and in the surface of the base metal. This deformation is known as the
=+35. According to the article “Modelling and Predicting the Effects of Submerged Arc Weldment Process Parameters on Weldment Characteristics and Shape Profiles” (J. of Engr. Manuf., 2012: 1230–1240), the submerged arc welding (SAW) process is commonly used for joining thick plates and
=+c. Does it appear that ICU stay for patients given the ventilation treatment is normally distributed? Explain your reasoning.
=+b. Answer the question posed in part (a) by carrying out a formal test of hypotheses. Is the result different from what you conjectured in part (a)?
=+a. Calculate a point estimate for the difference between true average ICU stay for the treatment and control groups. Does this estimate suggest that there is a significant difference between true average stays under the two conditions?
=+and a treatment group, each consisting of 60 of the patients. The sample mean ICU stay (days) and sample standard deviation for the treatment group were 19.9 and 39.1, respectively, whereas these values for the control group were 13.7 and 15.8.
=+34. The article “Evaluation of a Ventilation Strategy to Prevent Barotrauma in Patients at High Risk for Acute Respiratory Distress Syndrome” (New England J. of Medicine, 1998: 355–358) reported on an experiment in which 120 patients with similar clinical features were randomly divided
=+is higher than that for EC connections (as stated in the article)? Carry out the appropriate test using a significance level of .01. In reaching your conclusion, what type of error might you have committed? Note:SAS reports the P-value for a two-tailed test.Type N Mean Std Dev Std Error 1 20
=+33. The article “The Influence of Corrosion Inhibitor and Surface Abrasion on the Failure of AluminumWired Twist-on Connections” (IEEE Trans. on Components, Hybrids, and Manuf. Tech., 1984: 20–25) reported data on potential drop measurements for one sample of connectors wired with alloy
=+ Assuming that both samples were selected from normal distributions, carry out a test of hypotheses to decide whether the true average work of adhesion for the glass substrate is more than 12 mJ/m2 higher than that for the steel substrate.
=+32. The article cited in Exercise 41 in Chapter 7 gave the following data on work of adhesion measurements (in mJ/m2) for samples of ultra-high performance concrete adhered to two types of substrates:Substrate Observations Steel: 107.1 109.5 107.4 106.8 108.1 Glass: 122.4 124.6 121.6 120.6 123.3
=+c. The sample mean and standard deviation for the high-quality sample are 1.508 and .444, respectively, and those for the poor-quality sample are 1.588 and .530. Use the two-sample t test to decide whether true average extensibility differs for the two types of fabrics.
=+b. Construct a comparative boxplot. Does it suggest that there is a difference between true average extensibility for high-quality fabric specimens and that for poor-quality specimens?
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