Concept explainers
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, which could be gold (G), silver (S), or bronze (B). Three categories were then established: 1. Rating is the same [(G,G), (B,B), (S,S)]; 2. Rating differs by one medal [(G,S), (S,G), (S,B), (B,S)]; and 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 nine medal pairs has probability 1/9. Carry out an appropriate chisquared test using a significance level of .10.
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Chapter 14 Solutions
Probability and Statistics for Engineering and the Sciences
- Suppose a researcher is interested inthe effectiveness in a new childhood exercise program implemented in a SRS of schools across a particular county. In order to test the hypothesis that the new program decreases BMI (Kg/m2), the researcher takes a SRS of children from schools where the program is employed and a SRS from schools that do not employ the program and compares the results. Assume the following table represents the SRSs of students and their BMIs. Student intervention group BMI (kg/m2) Student control group BMI (kg/m2) A 18.6 A 21.6 B 18.2 B 18.9 C 19.5 C 19.4 D 18.9 D 22.6 E 24.1 F 23.6 A) Assuming that all the necessary conditions are met (normality, independence, etc.) carry out the appropriate statistical test to determine if the new exercise program is effective. Use an alpha level of 0.05. Do not assume equal variances.B) Construct a 95% confidence interval about your estimate for the average difference in BMI between the groups.arrow_forwardDo the results of your hypothesis test provide evidence that penetration of Fuentes’ Candied Bacon Potato Chips in grocery stores differs across its eight U.S. sales regions? In which sales region(s) is penetration of Fuentes’ Candied Bacon Potato Chips lower or higher than expected? Use the Marascuilo pairwise comparison procedure at a 5 .05 to test for differences between regions. New England Mid-Atlantic Midwest Great Plains South Atlantic Deep South Mountain Pacific Yes Yes No No Yes Yes Yes No No Yes Yes Yes Yes Yes Yes No Yes Yes No Yes No Yes No No Yes No Yes Yes Yes Yes Yes No Yes Yes No Yes Yes Yes No Yes No No No Yes No Yes No No Yes Yes Yes Yes Yes Yes Yes No No Yes Yes No Yes No Yes Yes Yes No No No Yes Yes Yes Yes Yes No No Yes Yes Yes No No Yes Yes Yes Yes Yes Yes No Yes Yes No No Yes Yes No Yes No No Yes Yes Yes Yes Yes No No No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes No Yes No No Yes Yes No No No Yes No Yes Yes…arrow_forwardThe accompanying data came from a study of collusion in bidding within the construction industry (“Detection of Collusive Behavior." J. of Construction Engr. and Mgmnt. 2012:1251- 1258)a. What proportion of the contracts involved at most five bidders? At least five bidders? b. What proportion of the contracts involved between five and 10 bidders, inclusive? Strictly between five and 10 bidders? c. Construct a histogram and comment on interesting features.arrow_forward
- A paper investigated the driving behavior of teenagers by observing their vehicles as they left a high school parking lot and then again at a site approximately 1 2 mile from the school. Assume that it is reasonable to regard the teen drivers in this study as representative of the population of teen drivers. MaleDriver FemaleDriver 1.3 -0.3 1.3 0.6 0.9 1.1 2.1 0.7 0.7 1.1 1.3 1.2 3 0.1 1.3 0.9 0.6 0.5 2.1 0.5 (a) Use a .01 level of significance for any hypothesis tests. Data consistent with summary quantities appearing in the paper are given in the table. The measurements represent the difference between the observed vehicle speed and the posted speed limit (in miles per hour) for a sample of male teenage drivers and a sample of female teenage drivers. (Use ?males − ?females. Round your test statistic to two decimal places. Round your degrees of freedom down to the nearest whole number. Round your p-value to three decimal places.) t = df =…arrow_forwardA paper investigated the driving behavior of teenagers by observing their vehicles as they left a high school parking lot and then again at a site approximately 1 2 mile from the school. Assume that it is reasonable to regard the teen drivers in this study as representative of the population of teen drivers. MaleDriver FemaleDriver 1.4 -0.2 1.2 0.5 0.9 1.1 2.1 0.7 0.7 1.1 1.3 1.2 3 0.1 1.3 0.9 0.6 0.5 2.1 0.5 (a) Use a .01 level of significance for any hypothesis tests. Data consistent with summary quantities appearing in the paper are given in the table. The measurements represent the difference between the observed vehicle speed and the posted speed limit (in miles per hour) for a sample of male teenage drivers and a sample of female teenage drivers. (Use ?males − ?females. Round your test statistic to two decimal places. Round your degrees of freedom down to the nearest whole number. Round your p-value to three decimal places.) t = df =…arrow_forwardAn automotive engineer is investigating two different types of metering devices for an electronic fuel injection system to determine whether they differ in their fuel mileage performance. The system is installed on 10 different cars, and a test is run with each metering device on each car. The data is provided below: Metering Device Car 1 2 1 17.6 16.8 2 19.4 20.0 3 18.2 17.6 4 17.1 16.4 5 15.3 16.0 6 15.9 15.9 7 16.3 16.5 8 18.0 18.4 9 17.3 16.4 10 19.1 20.1 Is there a significant difference between the means of the two metering devices? Use . Interpret the result in the context of the problem. An article in the journal Hazardous Waste and Hazardous Materials (Vol. 6, 1989) reported the results of an analysis of the weight of calcium in standard cement and cement doped with lead. Reduced levels of calcium would indicate that the hydration mechanism in the cement is blocked…arrow_forward
- The following table contains the results of a survey of daily rental rates of a mid-size car for three major rental car companies at three airport locations on three different days during the year. Is there sufficient evidence to conclude that there is a significant difference among the average daily rental rates for mid-size cars for the three rental car companies? Daily Rental Rates of Mid-Size Cars ($) New York Chicago Miami Hertz 83.9983.99 81.9981.99 73.9973.99 89.9989.99 91.9991.99 45.9945.99 77.9977.99 89.9989.99 72.9972.99 Avis 75.8675.86 77.9977.99 70.9970.99 45.1045.10 86.9986.99 60.9960.99 48.9848.98 97.9997.99 90.9990.99 National 80.0080.00 75.9975.99 57.0057.00 56.0056.00 71.0071.00 53.9953.99 56.0056.00 77.9977.99 67.9967.99 Copy Data ANOVA Source of Variation SSSS dfdf MSMS Company 709.6404709.6404 22 354.8202354.8202 Location 1631.71781631.7178 22 815.8589815.8589 Interaction 1157.83361157.8336 44 289.4584289.4584 Within…arrow_forwardThe article “HIV-positive Smokers Considering Quitting: Differences by Race/Ethnicity” (E. Lloyd-Richardson, C. Stanton, et al., Am J Health Behav, 2008:3–15) reported that in a group of 230 European-American HIV-positive smokers, 102 of them had used a nicotine patch to try to quit smoking, and in a group of 72 Hispanic-American HIV-positive smokers, 20 had used a nicotine patch. Can you conclude that the proportion of patch users is greater among European-Americans?arrow_forwardThree experiments investigating the relation between need for cognitive closure and persuasion were reported in “Motivated Resistance and Openness to Persuasion in the Presence or Absence of Prior Information,” by A. W. Kruglanski (Journal of Personality and Social Psychology, Vol. 65, No. 5, pp. 861–874). Part of the study involved administering a “need for closure scale” to a group of students enrolled in an introductory psychology course. The “need for closure scale” has scores ranging from 101 to 201. For the 73 students in the highest quartile of the distribution, the mean score was 178.70 . Assume a population standard deviation of 7.81. These students were all classified as high on their need for closure. Assume that the 73 students represent a random sample of all students who are classified as high on their need for closure. Find a 95% confidence interval for the population mean score on the “need for closure scale” for all students with a high need for closurearrow_forward
- A marketing firm wants to know if there is a difference in the best marketing strategy for new customers compared to returning customers. In order to determine the relationship between marketing strategy and customer type, the following information on number of sales generated is obtained for each group. Is there sufficient evidence at the 0.010.01 level of significance to conclude that an association exists between marketing strategy and customer type? Observed Sample of Customers Paid search Social Media Web retargeting Total New customer 167167 154154 140140 461461 Returning customer 146146 145145 164164 455455 Total 313313 299299 304304 916916 Copy Data Step 1 of 4 : Calculate the expected value for the number of sales generated by the web retargeting strategy for new customers. Round your answer to six decimal places.arrow_forwardThe article “The Effects of a Low-Fat, Plant-Based DietaryIntervention on Body Weight, Metabolism, and InsulinSensitivity in Postmenopausal Women” (Amer. J. of Med.,2005: 991–997) reported on the results of an experiment inwhich half of the individuals in a group of 64 postmenopausaloverweight women were randomly assigned to a particularvegan diet, and the other half received a diet based on NationalCholesterol Education Program guidelines. The sample meandecrease in body weight for those on the vegan diet was 5.8kg, and the sample SD was 3.2, whereas for those on the control diet, the sample mean weight loss and standard deviationwere 3.8 and 2.8, respectively. Does it appear the true averageweight loss for the vegan diet exceeds that for the control dietby more than 1 kg? Carry out an appropriate test of hypotheses at significance level .05 based on calculating a P-valuearrow_forwardThe article “Effects of Diets with Whole Plant-Origin Proteins Added with Different Ratiosof Taurine:Methionine on the Growth, Macrophage Activity and Antioxidant Capacity ofRainbow Trout (Oncorhynchus mykiss) Fingerlings” (O. Hernandez, L. Hernandez, et al.,Veterinary and Animal Science, 2017:4-9) reports that a sample of 210 juvenile rainbowtrout fed a diet fortified with equal amounts of the amino acids taurine and methionine for aperiod of 70 days had a mean weight gain of 313 percent with a standard deviation of 25, while 210 fish fed with a control diet had a mean weight gain of 233 percent with a standard deviation of 19. Units are percent. Find a 99% confidence interval for the difference in weight gain on the two diets.arrow_forward
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