Q&A Hero

Q: In a one-way ANOVA, which of the following is true? A) The degrees of freedom associated with the between sum of squares is equal to one less than the number of populations. B) The critical value will be an F-value from the F distribution. C) If the null hypothesis is rejected, it may still be possible that two or more of the population means are equal. D) All of the above

Q: In a one-way design, which of the following is true? A) The populations must have equal means. B) The sample sizes must be equal. C) The mean squares between will be larger than the mean squares within if the null hypothesis is rejected. D) The sample sizes must all differ.

Q: In order for a one-way analysis of variance to be considered a balanced design, which of the following must hold? A) The population variances must be equal. B) The sample sizes selected from each population must be equal. C) The study must have the same number of rows as it does columns. D) All of the above are true.

Q: A fast food chain operation is interested in determining whether the mean per customer purchase differs by day of the week. To test this, it has selected random samples of customers for each day of the week. The analysts then ran a one-way analysis of variance generating the following output:ANOVA: Single FactorBased upon this output, which of the following statements is true if the test is conducted at the 0.05 level of significance?A) There is no basis for concluding that mean sales is different for the different days of the week.B) Based on the p-value, the null hypothesis should be rejected since the p-value exceeds the alpha level.C) The experiment is conducted as an unbalanced design.D) Based on the critical value, the null should be rejected.

Q: An Internet service provider is interested in testing to see if there is a difference in the mean weekly connect time for users who come into the service through a dial-up line, DSL, or cable Internet. To test this, the ISP has selected random samples from each category of user and recorded the connect time during a week period. The following data were collected:Based upon these data and a significance level of 0.05, which of the following statements is true?A) The F-critical value for the test is 3.555B) The test statistic is approximately 43.9C) The null hypothesis should be rejected and conclude that the mean connect times for the three user categories are not all equal.D) All of the above are true.

Q: Assume you are conducting a one-way analysis of variance using a 0.05 level of significance and have found that the p-value = 0.02. Which of the follow is correct regarding what you can conclude? A) Do not reject the null hypothesis; the means are all the same. B) Reject the null hypothesis; the means are not all the same. C) Do not reject the null hypothesis; the means are not all the same. D) Reject the null hypothesis; the means are all the same.

Q: In a one-way analysis of variance test in which the levels of the factor being analyzed are randomly selected from a large set of possible factors, the design is referred to as: A) a fixed-effects design. B) a random-effects design. C) an undetermined results design. D) a balanced design.

Q: The State Transportation Department is thinking of changing its speed limit signs. It is considering two new options in addition to the existing sign design. At question is whether the three sign designs will produce the same mean speed. To test this, the department has conducted a limited test in which a stretch of roadway was selected. With the original signs up, a random sample of 30 cars was selected and the speeds were measured. Then, on different days, the two new designs were installed, 30 cars each day were sampled, and their speeds were recorded. Suppose that the following summary statistics were computed based on the data:Based on these sample results and a significance level equal to 0.05, assuming that the null hypothesis of equal means has been rejected, the Tukey-Kramer critical range is:A) 1.96.B) approximately 4.0.C) Can't be determined without more informationD) None of the above

Q: In conducting a one-way analysis of variance where the test statistic is less than the critical value, which of the following is correct? A) Conclude that the means are not all the same and that that the Tukey-Kramer procedure should be conducted. B) Conclude that the means are not all the same and that that the Tukey-Kramer procedure is not needed. C) Conclude that all means are the same and that the Tukey-Kramer procedure should be conducted. D) Conclude that all means are the same and there is no need to conduct the Tukey-Kramer procedure.

Q: A hotel chain has four hotels in Oregon. The general manager is interested in determining whether the mean length of stay is the same or different for the four hotels. She selects a random sample of n = 20 guests at each hotel and determines the number of nights they stayed. Assuming that she plans to test this using an alpha level equal to 0.05, which of the following is the appropriate alternative hypothesis? A) H0: μ1= μ2= μ3= μ4 B) H0: μ1≠ μ2≠ μ3≠ μ4 C) Not all population means are equal. D) σ1= σ2= σ3= σ4

Q: Which of the following is an assumption for the one-way analysis of variance experimental design? A) All populations are normally distributed. B) The populations have equal variances. C) The observations are independent. D) All of the above

Q: In a two-factor ANOVA design with replication, if the null hypothesis pertaining to interaction between factors A and B is rejected, then it is recommended that the hypothesis tests for factor A and factor B individually should not be conducted because the conclusions might be misleading.

Q: In a two-factor ANOVA design with replication, the null hypothesis for testing whether interaction exists is that no interaction exists. The alternative hypothesis is that interaction does exist.

Q: In a two-factor ANOVA with replication in which all hypotheses are to be tested using an alpha = .05 level, if the p-value for interaction is .03467, the decision maker should conclude that no interaction is present.

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. Assume that results show that there is an interaction. This would mean that, for example, which restaurant is rated the highest depends on which critic does the rating.

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: 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: 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.

Q: Given the partially completed ANOVA table below, the test statistic for determining if there is any blocking effect is F = 4.38.

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.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: 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: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: 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: 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.

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.

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: 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: Based on this information, what is the critical value that will be used to test the hypothesis?A) = 3.55B) = 2.832C) z = 1.645D) = 3.237

Q: Which distribution is used in testing the hypotheses about the equality of two population variances? A) z-distribution B) F-distribution C) x2distribution 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: σ2= 0.05 HA: σ2≠ 0.05 What is the upper tail critical value? A) 23.685 B) 24.996 C) 27.488 D) 26.119

Q: A manufacturer of industrial plywood has a contract to supply a boat maker with a large amount of plywood. One of the specifications calls for the standard deviation in thickness to not exceed .03 inch. A sample of n = 30 sheets was sampled randomly from a recent production run. The mean thickness was right at the 3/4 inch target thickness and the sample standard deviation was .05 inch. Testing at the 0.05 level of significance, which of the following is true? A) The test statistic is approximately 80.56. B) The critical value is approximately χ2= 43.773. C) The test statistic is approximately 48.333. D) Based on the sample data, there is no evidence to suggest that the plywood is not meeting the specifications.

Q: If a hypothesis test for a single population variance is to be conducted, which of the following statements is true? A) The null hypothesis must be stated in terms of the population variance. B) The chi-square distribution is used. C) If the sample size is increased, the critical value is also increased for a given level of statistical significance. D) All of the above are true.

Q: A fast food restaurant that sells burritos is concerned about the variability in the amount of filling that different employees place in the burritos. To achieve product consistency it needs this variability to be no more than 1.7 ounces. A sample of n = 18 burritos showed a sample variance of 2.89 ounces. Using a 0.10 level of significance, what can you conclude? A) The standards are being met since (test statistic) < (critical value). B) The standards are not being met since (test statistic) > (critical value). C) The standards are being met since (test statistic) > (critical value). D) The standards are not being met since (test statistic) < (critical value).

Q: A potato chip manufacturer has found that in the past the standard deviation of bag weight has been 0.2 ounce. They want to test whether the standard deviation has changed. The null hypothesis is: A) H0: σ2= 0.2 B) H0: σ = 0.2 C) H0: σ = 0.04 D) H0: σ2= 0.04

Q: When conducting a one-tailed hypothesis test of a population variance using a sample size of n = 24 and a 0.10 level of significance, the critical value is: A) 32.0069 B) 35.1725 C) 33.1962 D) 36.4150

Q: When a hypothesis test is to be conducted regarding a population variance, the test statistic will be: A) a t-value from the t-distribution. B) an x2value from the chi-square distribution. C) a z-value from the standard normal distribution. D) a binomial distribution p value.

Q: An analyst plans to test whether the standard deviation for the time it takes bank tellers to provide service to customers exceeds the standard of 1.5 minutes. The correct null and alternative hypotheses for this test are: A) H0: σ > 1.5 HA: σ ≥ 1.5 B) H0: σ ≤ 1.5 HA: σ > 1.5 C) H0: σ2≤ 2.25 HA: σ2> 2.25 D) H0: σ2> 2.25 HA: σ2≤ 2.25

Q: The F test statistic for testing whether the variances of two populations are the same is always positive.

Q: There is interest at the American Savings and Loan as to whether there is a difference between average daily balances in checking accounts that are joint accounts (two or more members per account) versus single accounts (one member per account). To test this, a random sample of checking accounts was selected with the following results:Based upon these data, if tested using a significance level equal to 0.10, the assumption of equal population variances should be rejected.

Q: A first step in testing whether two populations have the same mean value using the t-distribution is to use the chi-square distribution to test whether the populations have equal variances.

Q: Because of the way the F-distribution is formed, all F-tests are one-tailed tests.

Q: The F-distribution can only have positive values.

Q: A frozen food company that makes burritos currently has employees making burritos by hand. It is considering purchasing equipment to automate the process and wants to determine if the automated process would result in lower variability of burrito weights. It takes a random sample from each process as shown below. Process 1 (by hand) Process 2 (automated) n = 10 n = 8 s = 0.22 ounces s = 0.16 ounces In conducting the hypothesis test, the test statistic is F = 1.375.

Q: One of the key quality characteristics in many service environments is that the variation in service time be reasonably small. Recently, a major amusement park company initiated a new line system at one of its parks. It then wished to compare this new system with the old system in place at a comparable park in another state. At issue is whether the standard deviation in waiting time is less under the new line system than under the old line system. The following information was collected:Assuming that it wishes to conduct the test using a 0.05 level of significance, the null hypothesis should be rejected since the test statistic exceeds the F-critical value from the F-distribution table.

Q: The logic behind the F-test for testing whether two populations have equal variances is to determine whether sample variances computed from random samples selected from the two populations differ due to sampling error, or whether the difference is more than can be attributed to sampling error alone, in which case, we conclude that the populations have different variances.

Q: In a two-tailed hypothesis test involving two population variances, if the null hypothesis is true then the F-test statistic should be approximately equal to 1.0.

Q: One of the major automobile makers has developed two new engines. At question is whether the two engines have the same variability with respect to miles per gallon. To test this using a 0.10 level of significance, the following information is available:Based on this situation and the information provided, the null hypothesis cannot be rejected and it is possible that the two engines produce the same variation in mpg.

Q: A two-tailed test for two population variances could have a null hypothesis like the following: