Q&A Hero

Q: The general idea is that interaction between two factors means that the effect due to one of the factors is not uniform across all levels of the other factor.

Q: A study recently conducted by a marketing firm analyzed three different advertising designs (factor A) and four different income levels (factor B) of potential customers. At each combination of factor A and factor B, 5 customers are observed and the number of products produced is recorded. Interaction between the two factors would exist if low income customers have higher mean buying when design 1 is used, but higher income customers have higher mean buying when designs 2 and 3 are used.

Q: In a two-factor ANOVA study, if the two factors do not interact, then neither factor A nor factor B can be considered statistically significant.

Q: Interaction is the term that is used in a two-factor ANOVA design when the two factors have different means.

Q: Six food critics each visited and rated four different restaurants. Each critic visited each restaurant on three separate occasions and recorded a score for each visit. The critical value for testing whether there is any difference among the four restaurants, using the 0.05 level of significance is approximately F = 2.8.

Q: A study recently conducted by a marketing firm analyzed three different advertising designs and four different income levels of potential customers. At each combination of factor A and factor B, 5 customers are observed and the number of products produced are recorded. The degrees of freedom for the MSE in this two-factor ANOVA design is 48.

Q: A study recently conducted by a marketing firm analyzed three different advertising designs and four different income levels of potential customers. At each combination of factor A and factor B, 5 customers are observed and the number of products produced are recorded. The total number of degrees of freedom associated with this two-factor ANOVA design is 59.

Q: In a two-factor ANOVA design, the variances of the populations are assumed to be equal unless there is interaction present.

Q: In a two-factor ANOVA design with replications, there are three hypotheses to be tested; test for factor A, test for factor B, and test for interaction between factors A and B.

Q: In a two-factor ANOVA, the total sum of squares can be partitioned into four parts; the variation due to factor A, the variation due to factor B, the variation due to blocking, and the error variation.

Q: In a two-factor ANOVA, the minimum number of replications required in any cell is two, but all cells must have the same number of replications.

Q: Six food critics each visited and rated four different restaurants. Each critic visited each restaurant on three separate occasions and recorded a score for each visit. The total number of degrees of freedom is 71.

Q: Six food critics each visited and rated four different restaurants. Each critic visited each restaurant on three separate occasions and recorded a score for each visit. The number of degrees of freedom in the interaction row of the ANOVA table is 15.

Q: Six food critics each visited and rated four different restaurants. Each critic visited each restaurant on three separate occasions and recorded a score for each visit. The correct method for analyzing this data is two-factor ANOVA.

Q: The number of cells in a two-factor analysis of variance design is equal to the number of levels of factor A plus the number of levels of factor B.

Q: In order to analyze any potential interactions between factors in an analysis of variance study, it is necessary to have at least two measurements at each level of each factor.

Q: To test for the stopping distances of four brake systems, 10 of the same make and model of car are selected randomly and then are assigned randomly to each of four brake systems. This is a randomized complete block design.

Q: Based on the partially completed ANOVA table below, we know that 3 samples are being compared using 9 blocks. Source SS df MS F Between blocks 387 9 Between samples 422 3 Within samples 265 27 Total 1374 39

Q: Given the partially completed ANOVA table below, the test statistic for determining if there is any blocking effect is F = 4.38. Source SS df MS F Between blocks 387 9 Between samples 422 3 Within samples 265 27 Total 1374 39

Q: An advertising company is interested in determining if there is a difference in the mean sales that will be generated for a soft drink company based on which shelf the soft drinks are located. There are four possible shelf levels. The ad company wants to control for store size. The following data reflect the sales for one week at each combination of shelf level and store size. Level 1 Level 2 Level 3 Level 4 Small Store 300 200 500 200 Medium Store 400 180 600 200 Large Store 600 300 900 400 Based on the experimental design, the managers should conclude that they were justified in blocking on store size if they test using a 0.05 level of significance.

Q: An advertising company is interested in determining if there is a difference in the mean sales that will be generated for a soft drink company based on which shelf the soft drinks are located. There are four possible shelf levels. The ad company wants to control for store size. The following data reflect the sales for one week at each combination of shelf level and store size. Level 1 Level 2 Level 3 Level 4 Small Store 300 200 500 200 Medium Store 400 180 600 200 Large Store 600 300 900 400 Based on the experimental design, the calculated F-test statistic value for testing whether blocking on store size was effective is approximately 16.3.

Q: An advertising company is interested in determining if there is a difference in the mean sales that will be generated for a soft drink company based on which shelf the soft drinks are located. There are four possible shelf levels. The ad company wants to control for store size. The following data reflect the sales for one week at each combination of shelf level and store size. Level 1 Level 2 Level 3 Level 4 Small Store 300 200 500 200 Medium Store 400 180 600 200 Large Store 600 300 900 400 Based on the experimental design, the number of treatments is two.

Q: A company has established an experiment with its production process in which three temperature settings are used and five elapsed times are used for each setting. The company then produces one product under each and measures the resulting strength of the product. The managers are mainly interested in determining whether the mean strength is the same at all temperature settings, but they know that controlling for process time is important. The following data were observed from the experiment: Temperature 1 Temperature 2 Temperature 3 Time 1 140 150 170 Time 2 160 160 180 Time 3 150 150 160 Time 4 170 140 180 Time 5 150 150 170 Based on these data and experimental design, for a significance level of 0.05, the managers should conclude that they were justified in blocking on the basis of processing time.

Q: Three brands of running shoes are each tested by 10 different runners. The amount of wear on the sole of the shoes is then measured. The objective is to determine if there is any difference among the three brands of shoes based on how long the soles last. The degrees of freedom for testing whether there is any blocking effect D1 = 9 and D2 = 18.

Q: Three brands of running shoes are each tested by 10 different runners. The amount of wear on the sole of the shoes is then measured. The objective is to determine if there is any difference among the three brands of shoes based on how long the soles last. The degrees of freedom for testing whether the brands of shoes differ are D1 = 9 and D2 = 2.

Q: A company has established an experiment with its production process in which three temperature settings are used and five elapsed times are used for each setting. The company then produces one product under each and measures the resulting strength of the product. The managers are mainly interested in determining whether the mean strength is the same at all temperature settings, but they know that controlling for process time is important. The following data were observed from the experiment: Temperature 1Temperature 2Temperature 3Time 1140150170Time 2160160180Time 3150150160Time 4170140180Time 5150150170Based on these data and experimental design, the primary null hypothesis to be tested isH0 : 1 = 2 = 3.

Q: A company has established an experiment with its production process in which three temperature settings are used and five elapsed times are used for each setting. The company then produces one product under each and measures the resulting strength of the product. This experimental design is called a randomized complete block design.

Q: Three brands of running shoes are each tested by 10 different runners. The amount of wear on the sole of the shoes is then measured. The objective is to determine if there is any difference among the three brands of shoes based on how long the soles last. The null hypothesis is:H0 : 1 = 2 = 3.

Q: Three brands of running shoes are each tested by 10 different runners. The amount of wear on the sole of the shoes is then measured. The objective is to determine if there is any difference among the three brands of shoes based on how long the soles last. This means that there is one factor with 10 levels and 3 blocks.

Q: A randomized complete block analysis of variance allows the analyst to control for sources of variation that might adversely affect the analysis by using the concept of paired samples.

Q: Analysis of variance can only be done for fixed effects.

Q: The experiment-wide error rate will be higher than the 0.05 significance level if the multiple comparison tests for the mean difference between any two populations use the 0.05 level.

Q: The Tukey-Kramer method for multiple comparisons can only be used when the analysis of variance design is balanced.

Q: As a step in establishing its rates, an automobile insurance company is interested in determining whether there is a difference in the mean highway speeds that drivers of different age groups drive. To help answer this question, it has selected a random sample of drivers in three age categories: under 21, 21-50, and over 50. The engineers then recorded the drivers' speeds at a designated point on a highway in the state. The subjects were unaware that their speed was being recorded. The following one-way ANOVA output was generated from the sample data. Based upon this output, it is possible that a Type II statistical error has been committed if the null hypothesis is tested at the alpha equal 0.05 level. ANOVA: Single Factor

Q: If the null hypothesis that all population means are equal is rejected by the analysis of variance F-test, the alternative hypothesis that all population means differ is concluded to be true.

Q: The Tukey-Kramer method for multiple comparison is used after the analysis of variance F-test has lead us to reject the null hypothesis that all population means are equal.

Q: A fixed effects analysis of variance differs from a random-effects analysis of variance in the way in which the sums of squares are computed.

Q: As a step in establishing its rates, an automobile insurance company is interested in determining whether there is a difference in the mean highway speeds that drivers of different age groups drive. To help answer this question, it has selected a random sample of drivers in three age categories: under 21, 21-50, and over 50. The engineers then recorded the drivers' speeds at a designated point on a highway in the state. The subjects were unaware that their speed was being recorded. The following one-way ANOVA output was generated from the sample data. Based upon this output, if the significance level is 0.05, the engineers should conclude that the mean speeds may all be equal since the p-value is less than alpha. ANOVA: Single Factor

Q: A chain of fast food restaurants wants to compare the average service times at three different restaurants. It wants to conduct a hypothesis test to determine if all three means are the same or not, at the 0.05 level of significance. If n = 7 observations are taken at each of the three restaurants, the critical value is F = 3.555.

Q: A national car rental agency is interested in determining whether the mean days that customers rent cars is the same between three of its major cities. The following data reflect the number of days people rented a car for a sample of people in each of three cities. Assuming that a one-way analysis of variance is to be performed, the value of the test statistic is approximately F = 3.4. Boston Dallas Seattle 5 7 7 3 7 5 7 11 8 1 5 11 2 7 3

Q: A national car rental agency is interested in determining whether the mean days that customers rent cars is the same between three of its major cities. The following data reflect the number of days people rented a car for a sample of people in each of three cities. Assuming that a one-way analysis of variance is to be performed, the total sum of squares is computed to be approximately 120.9. Boston Dallas Seattle 5 7 7 3 7 5 7 11 8 1 5 11 2 7 3

Q: A national car rental agency is interested in determining whether the mean days that customers rent cars is the same between three of its major cities. The following data reflect the number of days people rented a car for a sample of people in each of three cities. Given this information, the correct null and alternative hypotheses are: H0 : 1 = 2 = 3 Ha : not all jare equal. Boston Dallas Seattle 5 7 7 3 7 5 7 11 8 1 5 11 2 7 3

Q: A chain of fast food restaurants wants to compare the average service times at four different restaurants. They want to conduct a hypothesis test to determine if all four means are the same or not. If n = 10 observations are taken at each of the four restaurants, then the degrees of freedom are D1 = 39 and D2 = 3.

Q: A study was recently conducted to see whether the mean starting salaries for graduates of engineering, business, healthcare, and computer information systems majors differ. A random sample of 8 graduates was selected from each major. The following chart shows some of the results of the ANOVA computations; however, some of the output is missing. Given what is available, the proper conclusion to reach based on the sample data is that the population means could be equal using a 0.05 level of significance. ANOVA: Single Factor

Q: A study was recently conducted to see whether the mean starting salaries for graduates of engineering, business, healthcare, and computer information systems majors differ. A random sample of 8 graduates was selected from each major. The following chart shows some of the results of the ANOVA computations; however, some of the output is missing. If it had been included, the calculated test statistic would be F = 8.33. ANOVA: Single Factor

Q: A study was recently conducted to see whether the mean starting salaries for graduates of engineering, business, healthcare, and computer information systems majors differ. A random sample of 8 graduates was selected from each major. Based upon this information, the appropriate null hypothesis to be tested is H0 : 1 - 2 - 3 - 4 = 0

Q: A study was recently conducted to see whether the mean starting salaries for graduates of engineering, business, healthcare, and computer information systems majors differ. A random sample of 8 graduates was selected from each major. The following shows the results of the ANOVA computations. However, the degrees of freedom column has been omitted. The correct number of degrees of freedom for the within variation is 28. ANOVA: Single Factor

Q: A study was recently conducted to see whether the mean starting salaries for graduates of engineering, business, healthcare, and computer information systems majors differ. A random sample of 8 graduates was selected from each major. If the test is to be conducted using an alpha = 0.05 level, the critical value will be F = 3.838.

Q: In conducting a one-way analysis of variance, if the null hypothesis is true then the variance between groups (MSB) should be approximately equal to the variance within groups (MSW).

Q: In one-way analysis of variance, the within-sample variation is not affected by whether the null hypothesis is true or not.

Q: In a one-way analysis of variance test, the following null and alternative hypotheses are appropriate: H0 : μ1 = μ2 = μ3 Hα : μ1 ≠μ2 ≠μ3

Q: Under the basic logic of one-way analysis of variance, if the within variation is large relative to the between variation, it is an indication that the population means are likely to be different.

Q: In a recent one-way ANOVA test, SSW was equal to 15,900 and the SSB was equal to 3,100. Therefore, SST is equal to 12,800.

Q: The within sample variation is the dispersion that exists because the sample means for the various factor levels are not all equal.

Q: In a one-way analysis of variance design, the total variation in the data across the various factor levels can be partitioned into two parts, the within sample variation and the between sample variation.

Q: In conducting one-way analysis of variance, the sample size for each group must be equal.

Q: In a completely randomized analysis of variance design, the observations from each factor are selected in an independent and random fashion.

Q: The one-way ANOVA test involves assuming that the population variances are equal.

Q: Recently, a company tested three different machine types to see if there was a difference in the mean thickness of products produced by the three. A random sample of ten products was selected from the output from each machine. Given this information, the proper design to test whether the means are equal is a one-way ANOVA balanced design.

Q: In conducing one-way analysis of variance, the population distributions are assumed normally distributed.

Q: In a one-way analysis of variance design, there is a single factor of interest but there may be multiple levels of the factor.

Q: The term one-way analysis of variance refers to the fact that in conducting the test, there is only one way to set up the null and alternative hypotheses.

Q: There are two major companies that provide SAT test tutoring for high school students. At issue is whether Company 1, which has been in business for the longer time, provides better results than Company 2, the newer company. Specifically of interest is whether the mean increase in SAT scores for students who have already taken the SAT test one time is higher for Company 1 than for Company 2. Two random samples of students are selected. The following data reflect the number of points higher (or lower) that the students scored on the SAT test after taking the tutoring. Prior to conducting the test, which compares the means, we should determine if the assumption of equal variances is supported.Conduct the appropriate hypothesis test to determine if the assumption of equal variances is supported using a 0.10 level of significance.Company 1Company 298656011-143080525527711637274147

Q: A PC company uses two suppliers for rechargeable batteries for its notebook computers. Two factors are important quality features of the batteries: mean use time and variation. It is desirable that the mean use time be high and the variability be low. Recently, the PC maker conducted a test on batteries from the two suppliers. In the test, 9 randomly selected batteries from Supplier 1 were tested and 12 randomly selected batteries from Supplier 2 were tested. The following results were observed:Supplier 1 Supplier 2n1 = 9 n2 = 121 = 67.25 min 2 = 72.4 mins1 = 11.2 min s2 = 9.9 minBased on these sample results, can the PC maker conclude that a difference exists between the two batteries with respect to the population mean use time? Test using a 0.10 level of significance.

Q: A PC company uses two suppliers for rechargeable batteries for its notebook computers. Two factors are important quality features of the batteries: mean use time and variation. It is desirable that the mean use time be high and the variability be low. Recently, the PC maker conducted a test on batteries from the two suppliers. In the test, 9 randomly selected batteries from Supplier 1 were tested and 12 randomly selected batteries from Supplier 2 were tested. The following results were observedSupplier 1 Supplier 2n1 = 9 n2 = 121 = 67.25 min 2 = 72.4 mins1 = 11.2 min s2 = 9.9 minBased on these sample results, can the PC maker conclude that a difference exists between the two batteries with respect to the population standard deviations? Test using a 0.10 level of significance.

Q: The Department of Weights and Measures in a southern state has the responsibility for making sure that all commercial weighing and measuring devices are working properly. For example, when a gasoline pump indicates that 1 gallon has been pumped, it is expected that 1 gallon of gasoline will actually have been pumped. The problem is that there is variation in the filling process. The state's standards call for the mean amount of gasoline to be 1.0 gallon with a standard deviation not to exceed 0.010 gallons. Recently, the department came to a gasoline station and filled 10 cans until the pump read 1.0 gallon. It then measured precisely the amount of gasoline in each can. The following data were recorded: 0.991 0.962 1.007 1.038 1.036 1.052 0.934 0.993 1.033 0.967 Based on these data, what should the Department of Weights and Measures conclude if it wishes to test whether the standard deviation exceeds 0.010 gallons or not, using a 0.05 level of significance?

Q: The U.S. Golf Association provides a number of services for its members. One of these is the evaluation of golf equipment to make sure that the equipment satisfies the rules of golf. For example, they regularly test the golf balls made by the various companies that sell balls in the United States. Recently, they undertook a study of two brands of golf balls with the objective to see whether there is a difference in the mean distance that the two golf ball brands will fly off the tee. To conduct the test, the U.S.G.A. uses a robot named "Iron Byron," which swings the club at the same speed and with the same swing pattern each time it is used. The following data reflect sample data for a random sample of balls of each brand. Brand A: 234 236 230 227 234 233 228 229 230 238 Brand B: 240 236 241 236 239 243 230 239 243 240 Given this information, what is the test statistic for testing whether the two population variances are equal? A) Approximately F = 1.145 B) t = 1.96 C) t = -4.04 D) None of the above

Q: A small business owner has two fast food restaurants. The owner wants to determine if there is any difference in the variability of service times at the drive-thru window of each restaurant. A sample of size n = 9 is taken from each restaurant's drive-thru window. To perform a hypothesis test using the 0.05 level of significance the critical value is: A) 3.438 B) 3.197 C) 4.026 D) 4.433

Q: Two airlines are being compared with respect to the time it takes them to turn a plane around from the time it lands until it takes off again. The study is interested in determining whether there is a difference in the variability between the two airlines. They wish to conduct the hypothesis test using an alpha = 0.02. If random samples of 20 flights are selected from each airline, what is the appropriate F critical value? A) 3.027 B) 2.938 C) 2.168 D) 2.124

Q: In performing a one-tailed test for the difference between two population variances, which of the following statements is true? A) The level of alpha needs to be doubled before finding the F-critical value in the table. B) The sample variance that is predicted to be larger in the alternative hypothesis goes in the numerator when forming the F-test statistic. C) You always place the larger of the two sample variances in the numerator. D) The alternative hypothesis must contain the equality.

Q: The Russet Potato Company has been working on the development of a new potato seed that is hoped to be an improvement over the existing seed that is being used. Specifically, the company hopes that the new seed will result in less variability in individual potato length than the existing seed without reducing the mean length. To test whether this is the case, a sample of each seed is used to grow potatoes to maturity. The following information is given: Old Seed New Seed Number of Seeds = 11 Number of Seeds = 16 Average length = 6.25 inches Average length = 5.95 inches Standard Deviation = 1.0 inches Standard Deviation = 0.80 inches The on these data, if the hypothesis test is conducted using a 0.05 level of significance, the calculated test statistic is: A) = 1.25 B) = 0.80 C) = 0.64 D) = 1.56

Q: The Russet Potato Company has been working on the development of a new potato seed that is hoped to be an improvement over the existing seed that is being used. Specifically, the company hopes that the new seed will result in less variability in individual potato length than the existing seed without reducing the mean length. To test whether this is the case, a sample of each seed is used to grow potatoes to maturity. The following information is given: Old SeedNew SeedNumber of Seeds = 11Number of Seeds = 16Average length = 6.25 inchesAverage length = 5.95 inchesStandard Deviation = 1.0 inchesStandard Deviation = 0.80 inchesThe correct null hypothesis for testing whether the variability of the new seed is less than the old seed is:

Q: It is believed that the SAT scores for students entering two state universities may have different standard deviations. Specifically, it is believed that the standard deviation at University A is greater than the standard deviation at University B. To test this using an alpha = 0.05 level, a sample of 14 student SAT scores from University A was selected and a sample of 8 SAT scores from University B was selected. The following sample results were observed: University A University B = 1104 = 1254 s = 134 s = 108 Based on this information, what is the value of the test statistic? A) 1.2407 B) 0.6496 C) 1.5394 D) None of the above.

Q: It is believed that the SAT scores for students entering two state universities may have different standard deviations. Specifically, it is believed that the standard deviation at University A is greater than the standard deviation at University B. To test this using an alpha = 0.05 level, a sample of 14 student SAT scores from University A was selected and a sample of 8 SAT scores from University B was selected. The following sample results were observed: University A University B = 1104 = 1254 s = 134 s = 108 Based on this information, what is the critical value that will be used to test the hypothesis? A) = 3.55 B) = 2.832 C) z = 1.645 D) = 3.237

Q: It is believed that the SAT scores for students entering two state universities may have different standard deviations. Specifically, it is believed that the standard deviation at University A is greater than the standard deviation at University B. If a statistical test is to be conducted, which of the following would be the proper way to formulate the null hypothesis?

Q: Which distribution is used in testing the hypotheses about the equality of two population variances? A) z-distribution B) F-distribution C) x2 distribution D) t-distribution

Q: Which of the following is the appropriate null hypothesis when testing whether two population variances are equal?

Q: If the variance of the contents of cans of orange juice is significantly more than 0.003, the manager has to order to stop the filling machine. A sample of 26 cans of orange juice showed a standard deviation of 0.06 ounce. Based on the sample and at the 0.05 level of significance, the filling machine should be A) stopped. B) kept going. C) upgraded. D) downgraded.

Q: A consulting report that was recently submitted to a company indicated that a hypothesis test for a single population variance was conducted. The report indicated that the test statistic was 34.79, the hypothesized variance was 345 and the sample variance 600. However, the report did not indicate what the sample size was. What was it? A) n = 100 B) Approximately n = 18 C) Approximately 21 D) Can't be determined without knowing what alpha is.

Q: To test the following hypotheses at the 0.05 level of significance, using a sample size of n = 15.H0 : 2 = 0.05HA : 2 0.05What is the upper tail critical value?A) 23.685B) 24.996C) 27.488D) 26.119