Q&A Hero

Q: The control limits in the x-bar chart are set so that 95 percent of the values will fall inside the control limits when there is only common cause variation.

Q: It is entirely possible for the R-chart to show that a process is in statistical control and the -chart to show that the same process is out of control.

Q: The frequency distribution of most processes' statistics will begin to resemble the shape of the normal distribution as the values are collected and grouped into classes.

Q: Both p-charts and c-charts are designed for use when the data we are working with are referred to as attribute data.

Q: A p-chart would potentially be used to monitor the diameters of bolts made by a bolt manufacturing plant.

Q: A stable process is typically defined as one in which all output is operating within 3 standard deviations of the process center.

Q: A stable process is one that has had all its variation removed through quality improvement efforts on the part of the organization.

Q: Total process variation is made up of the sum of common cause variation and special cause variation.

Q: One of the most common sources of common cause variation is the people who are working in the process.

Q: If a process control chart has only one point outside the upper or lower control limits, there is insufficient evidence to conclude that the process was out of control at the time that the measurement was taken.

Q: Process control charts are used to provide signals to indicate when the output of a process is out of control.

Q: The six most common sources of variation are people, machines, materials, methods, measurement, and environment.

Q: In process improvement efforts, the goal is to first remove the common cause variation and then to reduce the special cause variation in a system.

Q: Common cause variation is variation in the output of a process that is unexpected and has an assignable cause.

Q: Special cause variation is variation in the output of a process that is naturally occurring and expected and that may be the result of random causes.

Q: Variation exists naturally in the world around us so all processes and products can be expected to vary.

Q: We expect virtually all the data in a stable process to fall within 2 standard deviations of the mean.

Q: A restaurant has three separate dining areas: the patio, the alcove, and the main hall. At question is whether the median dollar amount per customer is the same or different between these three restaurant locations. To test this, the manager has randomly selected samples from each location. These data are shown as follows: Patio Alcove Main Hall $22.45 $20.20 $40.00 $35.70 $19.50 $18.50 $17.90 $30.00 $19.60 $25.50 $18.25 $34.50 $19.50 $22.50 $32.00 $14.50 $14.50 $28.70 $30.20 $17.80 $25.00 $36.50 $21.30 $15.75 a. If the manager is unwilling to make the assumption that the bill amounts are normally distributed at all three locations, what statistical technique would you suggest to test whether the median bill amounts are the same or different? b. State the appropriate null and alternative hypotheses. c. Using an alpha level equal to .05, test the null hypothesis and state your conclusion.

Q: A paint manufacturer is interested in determining whether there is a difference in the median time it takes for two different brands of paint to dry once they have been applied to a wall surface. To test this, the company has selected a random sample of 5 walls and applied brand 1 and another 5 walls and applied brand 2. The following data reflect the actual drying time in hours: Brand 1 Brand 2 3.4 2.0 3.2 3.0 2.8 3.0 3.7 2.2 2.5 2.1 a. If you are unwilling to make the assumptions necessary to use a t-test, what test would you recommend in this situation? b. What would be the appropriate null and alternative hypothesis? c. Using an alpha level equal to .05, conduct the hypothesis test and state the conclusion.

Q: A real estate broker claims that the median days that one of his listings stays on the market is 45 or less days. To test this, he has collected the following random sample of properties sold showing the days they were on the market prior to selling:Days5030702030406080The broker is unwilling to assume that the population data are normally distributed.a. What is the correct null and alternative hypothesis to be tested?b. What statistical test would you recommend be used to test this hypothesis?c. Conduct the test and indicate what conclusion should be reached if we test at an alpha = .05 level?

Q: Under what conditions should a decision maker use a nonparametric statistical procedure?

Q: A survey was recently conducted in which random samples of car owners of Chrysler, GM, and Ford cars were surveyed to determine their satisfaction. Each owner was asked to rate overall satisfaction on a scale of 1 (poor) to 1000 (excellent). The following data were recorded: Chrysler GM Ford 650 400 700 700 800 750 500 500 650 800 400 800 900 600 900 750 900 700 If the analysts are not willing to assume that the population ratings are normally distributed and will use the Kruskal-Wallis test to determine if the three companies have different median ratings, what is the correct conclusion if the test is to be conducted using an alpha = .05 level? A) H0 should be rejected and we conclude that there is no significant difference between the 3 companies. B) H0 should not be rejected and we conclude that there is no significant difference between the 3 companies. C) H0 should be rejected and we conclude that there is a significant difference between the 3 companies. D) H0 should not be rejected and we conclude that there is a significant difference between the 3 companies.

Q: A survey was recently conducted in which random samples of car owners of Chrysler, GM, and Ford cars were surveyed to determine their satisfaction. Each owner was asked to rate overall satisfaction on a scale of 1 (poor) to 1000 (excellent). The following data were recorded: Chrysler GM Ford 650 400 700 700 800 750 500 500 650 800 400 800 900 600 900 750 900 700 If the analysts are not willing to assume that the population ratings are normally distributed and will use the Kruskal-Wallis test to determine if the three companies have different median ratings, what is correct test statistic for these data? A) H = 1.965 B) t = 1.96 C) H = 3.34 D) H = .65

Q: A survey was recently conducted in which random samples of car owners of Chrysler, GM, and Ford cars were surveyed to determine their satisfaction. Each owner was asked to rate overall satisfaction on a scale of 1 (poor) to 1000 (excellent). The following data were recorded:ChryslerGMFord650400700700800750500500650800400800900600900750900700If the analysts are not willing to assume that the population ratings are normally distributed and will use the Kruskal-Wallis test to determine if the three companies have different median ratings, what is the appropriate critical value if the test is to be conducted using an alpha = .05 level?A) x2= 5.05B) x2 = 5.99C) x2 = 24.99D) x2= 3.67

Q: A survey was recently conducted in which random samples of car owners of Chrysler, GM, and Ford cars were surveyed to determine their satisfaction. Each owner was asked to rate overall satisfaction on a scale of 1 (poor) to 1000 (excellent). The following data were recorded: Chrysler GM Ford 650 400 700 700 800 750 500 500 650 800 400 800 900 600 900 750 900 700 If the analysts are not willing to assume that the population ratings are normally distributed and will use the Kruskal-Wallis test to determine if the three companies have different median ratings, which company has the smallest sum of ranks? A) Chrysler B) GM C) Ford D) All three are equal.

Q: If we are interested in testing to determine whether the center of three or more populations is equal when the data in the samples are ordinal, what is the appropriate test to conduct? A) A t-test B) An ANOVA C) A Kruskal-Wallis D) A Wilcoxon Matched-Pairs Sign Rank test

Q: Assume that a Kruskal-Wallis test is being conducted to determine whether or not the medians of three populations are equal. The sum of rankings and the sample size for each group are below. Group 1 Group 2 Group 3 R1 = 60 R2 = 36 R3 = 24 n1 = 6 n2 = 5 n3 = 4 What is the critical value for this test using a 0.10 level of significance? A) 6.2514 B) 5.9915 C) 7.8147 D) 4.6052

Q: Assume that a Kruskal-Wallis test is being conducted to determine whether or not the medians of three populations are equal. The sum of rankings and the sample size for each group are below. Group 1 Group 2 Group 3 R1 = 60 R2 = 36 R3 = 24 n1 = 6 n2 = 5 n3 = 4 What is the value of the test statistic? A) 7.8147 B) 2.16 C) 48.68 D) 12.59

Q: Assume that 4 populations are to be compared using a Kruskal-Wallis one-way analysis of variance. What is the critical value using a 0.05 level of significance? A) 5.9915 B) 6.2514 C) 7.8147 D) 9.4877

Q: In a Kruskal-Wallis test when ties occur, each observation is given the ________ for which it is tied. A) highest rank B) lowest rank C) mean rank D) median rank

Q: The Kruskal-Wallis test is usually limited to comparing sample values from ________ or more populations. A) 2 B) 3 C) 4 D) 5

Q: Which of the following is not an assumption of the Kruskal-Wallis one-way analysis of variance? A) Variables have a continuous distribution. B) Samples are independent. C) Sample sizes are equal for all populations. D) Population distributions are identical except for possible differences in center.

Q: In conducting a Kruskal-Wallis one-way analysis of variance, the test statistic is assumed to have approximately which distribution when the null hypothesis is true? A) A t-distribution B) An F-distribution C) A normal distribution D) A chi-square distribution

Q: If a Mann-Whitney U test was performed and U1 = 50 and U2 = 40, if the sample from population 1 was 10, the sample size from population 2 was: A) 10 B) 15 C) 9 D) Can't be determined without more information.

Q: When employing a small sample Mann-Whitney U test for a two-tailed test, which of the following is true? A) The sample sizes need to be equal. B) Select as the test statistic the smaller of the two U values. C) Select either of the U values to be the test statistic. D) The alpha level should be doubled.

Q: The Wilcoxon matched-pairs signed rank test assumes that the two samples are: A) equal in size. B) independent and random. C) paired. D) Both A and C

Q: The Mann-Whitney U test assumes that the 2 samples are: A) equal in size. B) independent and random. C) matched or paired. D) normally distributed.

Q: If a two-tailed Wilcoxon Matched-Pairs Signed Rank test is conducted for a sample of n = 8 and an alpha level equal to .05, the critical value is: A) 4 B) 1.96 C) 30 D) 2

Q: If we wish to test whether two related populations have equal medians, an appropriate nonparametric test to use is: A) the Mann-Whitney U test. B) the Kruskal-Wallis test. C) the Wilcoxon signed rank test. D) the Wilcoxon matched-pairs signed rank test.

Q: Assume that you are conducting a small sample Mann-Whitney U test where n1 = 14 and n2 = 16 and that U1 = 98. Assuming that U1 has been found correctly, what is the value of U2? A) 112 B) 126 C) 224 D) Insufficient information to determine U2.

Q: Recently, a legislative committee commissioned a study of incomes in a western state. At issue was whether the ratings of the legislature's performance differed between rural citizens and city residents. A random sample of 25 city residents and 35 rural residents was asked to rate the performance of the legislature on a scale of 1 to 100. The analysts believe that the population distribution of ratings would be highly skewed so they decided to use the Mann-Whiney U test to test whether there is a difference in median ratings by the two groups. Given this information, which of the following is the correct critical value if the test is to be conducted at the .10 level of significance? A) z = 1.96 B) t = 2.0357 C) U = 437.5 D) z = 1.645

Q: In a large sample Mann-Whitney U test in which the sample size from the first population is 30 and the sample size from the second population is 40, which of the following is the expected U value if the null hypothesis of equal median values is true? A) 1,200 B) 70 C) 35 D) 600

Q: Consider the situation in which a human resources manager wishes to determine whether the median number of days of sick leave per year is greater for female employees than for male employees. The following data represent random samples of males and females: Males Females 5 14 10 5 0 13 9 7 2 8 7 0 5 7 10 10 3 6 1 5 If the manager is unwilling to assume that the populations are normally distributed, which of the following is the correct conclusion to reach if the test is conducted using a .05 level of significance? A) Reject the null hypothesis B) Conclude that females do have a higher median than males C) Do not reject the null hypothesis D) Conclude that males have a higher median than females

Q: Assume you are conducting a two-tailed Mann-Whitney U test for a small sample and have found that U1 = 58 and U2 = 86. What is the value of the test statistic? A) 58 B) 86 C) 72 D) 144

Q: Consider the situation in which a human resources manager wishes to determine whether the median number of days of sick leave per year is the same for female employees as for male employees. The following data represent random samples of males and females: MalesFemales5141050139728705710103615If the manager is unwilling to assume that the populations are normally distributed, which of the following would be the appropriate null hypothesis to be tested?A) H0 : = 0B) H0 : = 0C) H0 : 1 = 2D) H0 : 1 = 2

Q: Under what circumstances should the standard normal distribution be used when employing the Mann-Whitney U test? A) When the sample sizes are equal from the two populations B) When the sample sizes are greater than 20 C) When the populations are normally distributed D) You would never use the standard normal distribution.

Q: Consider the situation in which a study was recently conducted to determine whether the median price of houses is the same in Seattle and Phoenix. The following data were collected. Seattle Phoenix 233,000 309,000 567,800 422,000 145,600 209,000 234,000 187,000 356,000 165,000 203,000 189,000 Given these data, if a Mann-Whitney U test is to be used, the test statistic is: A) 22 B) 14 C) approximately 1.96 D) 34

Q: Consider the situation in which a study was recently conducted to determine whether the median price of houses is the same in Seattle and Phoenix. The following data were collected. Seattle Phoenix 233,000 309,000 567,800 422,000 145,600 209,000 234,000 187,000 356,000 165,000 203,000 189,000 Given these data, if a Mann-Whitney U test is to be used, the U statistic for Seattle is: A) 45 B) 35 C) 22 D) 14

Q: Consider the situation in which a study was recently conducted to determine whether the median price of houses is the same in Seattle and Phoenix. The following data were collected. Seattle Phoenix 233,000 309,000 567,800 422,000 145,600 209,000 234,000 187,000 356,000 165,000 203,000 189,000 Given these data, if a Mann-Whitney U test is to be used, the U statistic for Phoenix is: A) 14 B) 22 C) 35 D) 27

Q: Consider the situation in which a study was recently conducted to determine whether the median price of houses is the same in Seattle and Phoenix. The following data were collected. Seattle Phoenix 233,000 309,000 567,800 422,000 145,600 209,000 234,000 187,000 356,000 165,000 203,000 189,000 Given these data, if a Mann-Whitney U test is to be used, the sum of the ranks for Seattle is: A) 43 B) 35 C) 25.5 D) 40

Q: Which of the following is not an assumption of the Mann-Whitney U test? A) The sample sizes are equal. B) The samples are independent. C) The value measured is continuous. D) The population distributions are the same for shape and spread.

Q: When the Mann-Whitney U test is performed, which of the following is true? A) We assume that the populations are normally distributed. B) We are interested in testing whether the medians from two populations are equal. C) The data are nominal level. D) The samples are independent.

Q: A marketing firm is interested to know whether the median age of college students is 21 years. A sample of 80 college students is taken. Thirty of the students were under 21, 45 of the students were over 21, and 10 were 21 years old. The conclusion is that A) the median age of college students is significantly different from 21. B) the median age of college students is not significantly different from 21. C) the median age of college students is significantly older than from 21. D) the median age of college students is significantly younger than from 21.

Q: Which of the following tests would not be an example of nonparametric method? A) Wilcoxon signed-rank test B) Mann-Whitney U-Test C) Kruskal-Wallis One-Way Analysis of Variance D) χ2 test

Q: In the finding the critical value for the Wilcoxon signed rank test, what does "n" represent? A) The number of observations in the sample B) The number of pairs C) The number of nonzero deviations D) The number of positive ranks

Q: The General Electric service department believes that the median time for a service call should be 30 or fewer minutes. To test this, the following random sample of service times was collected: Time 33 27 40 34 22 19 40 73 26 Given that the managers do not wish to make the assumption that the population is normally distributed, the test statistic for the Wilcoxon signed rank sum test is: A) W = 43.0 B) W = 27.0 C) W = 18.0 D) None of the above

Q: The General Electric service department believes that the median time for a service call should be 30 or fewer minutes. To test this, the following random sample of service times was collected: Time 33 27 40 34 22 19 40 73 26 Given that the managers do not wish to make the assumption that the population is normally distributed, the critical value for the test about median service times, using a .05 level of significance, is: A) 5 B) 40 C) 8 D) 37

Q: The General Electric service department believes that the median time for a service call should be 30 or fewer minutes. To test this, the following random sample of service times was collected: Time 33 27 40 34 22 19 40 73 26 Given that the managers do not wish to make the assumption that the population is normally distributed, the appropriate statistical test for testing about service times is: A) the t-test. B) the Kruskal-Wallis test. C) the Wilcoxon signed rank sum test. D) the F-test.

Q: The Wilcoxon signed rank test is used to test which of the following type of hypotheses? A) Tests about a single population median B) Tests involving three or more population medians C) Tests about the variances of two or more populations D) Tests about two or more population proportions

Q: Which of the following is not a step involved in the Wilcoxon signed rank test? A) Find the deviations from the hypothesized median B) Rank the deviations C) Convert the deviations to absolute values D) Find the deviations from the sample median

Q: Nonparametric statistical tests are used when: A) the sample sizes are small. B) we are unwilling to make the assumptions of parametric tests. C) the standard normal distribution cannot be computed. D) the population parameters are unknown.

Q: If you are interested in testing whether the median of a population is equal to a specific value, an appropriate test to use is: A) the Mann-Whitney U test. B) the t-test. C) the Wilcoxon signed rank test. D) the Wilcoxon Matched-Pairs Signed Rank test.

Q: Kruskal-Wallis One-Way Analysis of Variance is the nonparametric counterpart to the one-way ANOVA procedure in which the assumptions of normally distributed populations with equal variances are satisfied.

Q: The makers of furnace filters recently conducted a test to determine whether the median number of particulates that would pass through their four leading filters was the same. A random sample of 6 of each type of filter was used with the following data being recorded: Filter 1 Filter 2 Filter 3 Filter 4 40 100 165 55 25 110 90 20 70 89 40 90 47 67 200 105 55 77 103 90 88 102 110 120 If the Kruskal-Wallis test is used with an alpha = .01, the null hypothesis should be rejected and the managers should conclude that the four filters do not allow an equal median number of particulates.

Q: The makers of furnace filters recently conducted a test to determine whether the median number of particulates that would pass through their four leading filters was the same. A random sample of 6 of each type of filter was used with the following data being recorded: Filter 1 Filter 2 Filter 3 Filter 4 40 100 165 55 25 110 90 20 70 89 40 90 47 67 200 105 55 77 103 90 88 102 110 120 If the Kruskal-Wallis test is used, the test statistic is approximately H = 7.814

Q: The makers of furnace filters recently conducted a test to determine whether the median number of particulates that would pass through their four leading filters was the same. A random sample of 6 of each type of filter was used with the following data being recorded: Filter 1 Filter 2 Filter 3 Filter 4 40 100 165 55 25 110 90 20 70 89 40 90 47 67 200 105 55 77 103 90 88 102 110 120 If the Kruskal-Wallis test is used, the critical value for an alpha = .05 is 7.814

Q: The makers of furnace filters recently conducted a test to determine whether the median number of particulates that would pass through their four leading filters was the same. A random sample of 6 of each type of filter was used with the following data being recorded: Filter 1 Filter 2 Filter 3 Filter 4 40 100 165 55 25 110 90 20 70 89 40 90 47 67 200 105 55 77 103 90 88 102 110 120 If the managers are unwilling to assume that the populations are normally distributed, the appropriate test in this case would be the Mann-Whitney U test.

Q: The makers of furnace filters recently conducted a test to determine whether the median number of particulates that would pass through their four leading filters was the same. A random sample of 6 of each type of filter was used with the following data being recorded: Filter 1 Filter 2 Filter 3 Filter 4 40 100 165 55 25 110 90 20 70 89 40 90 47 67 200 105 55 77 103 90 88 102 110 120 The Kruskal-Wallis test can be used in this case since it requires that the sample sizes be equal.

Q: Assume that a Kruskal-Wallis test is being conducted to determine whether or not the medians of three populations are equal. The sum of rankings and the sample size for each group are below. Group 1 Group 2 Group 3 R1 = 60 R2 = 36 R3 = 24 n1 = 6 n2 = 5 n3 = 4 The value of the test statistic is H = 0.68

Q: A recent study was conducted to determine if any of three suppliers of electronic components has a different median delivery time on special orders. To test this, five orders were given to each supplier and the delivery days were recorded. These data are shown as follows: Supplier 1 Supplier 2 Supplier 3 15 11 15 19 7 9 13 19 5 10 10 12 20 12 10 If a Kruskal-Wallis test is to be performed, the sum of the rankings for Supplier 1 is 45.

Q: A recent study was conducted to determine if any of three suppliers of electronic components has a different median delivery time on special orders. To test this, five orders were given to each supplier and the delivery days were recorded. These data are shown as follows: Supplier 1 Supplier 2 Supplier 3 15 11 15 19 7 9 13 19 5 10 10 12 20 12 10 If a Kruskal-Wallis test is to be performed, the number of degrees of freedom for determining the critical value is 2.

Q: A recent study was conducted to determine if any of three suppliers of electronic components has a different median delivery time on special orders. To test this, five orders were given to each supplier and the delivery days were recorded. These data are shown as follows: Supplier 1 Supplier 2 Supplier 3 15 11 15 19 7 9 13 19 5 10 10 12 20 12 10 If a Kruskal-Wallis test is to be performed, the critical value for a test conducted using an alpha = .05 level is χ2 = 11.0705

Q: The critical value for a Kruskal Wallis test is an F value from the F-distribution.

Q: In using the Kruskal-Wallis test the sample sizes for each population must be equal.

Q: The Kruskal-Wallis test is used to test whether the centers of 3 or more populations are equal so long as that is the only possible difference between the population distributions.

Q: If a decision maker wishes to test whether four independent populations have the same center and is unwilling to make the assumption that the populations are normally distributed with equal variances, she can use the Kruskal-Wallis test.

Q: The distribution of T-values in the Wilcoxon Matched-Pairs Signed Rank test is approximately normal if the sample size (number of matched pairs) exceeds 25.

Q: When testing whether two paired populations have equal medians and the sample sizes are large, it is appropriate to convert the Wilcoxon Matched-Pairs Signed Rank test to a paired sample t-test.

Q: In conducting the Wilcoxon Matched-Pairs Signed Rank test, the difference between each pair of values must be found prior to conducting any ranking.

Q: In order to determine whether the median distance for the X-Special golf ball exceeds the median distance for the best-selling golf ball, six golfers were selected and asked to hit each ball with their driver. The distance was recorded. The following data were observed. Golfer X-Special Best Seller 1 240 233 2 267 270 3 255 240 4 234 230 5 250 260 6 285 270 Based on these data, and testing at an alpha = 0.025 level, the critical value for the Wilcoxon Matched Pairs Signed Rank test is 2.