Finance

Q: Consider the following calculations for a one-way analysis of variance from a completely randomized design with 20 total observations. The response variable is sales in millions of dollars and the four treatment levels represent the four regions that the company serves. Perform a pairwise comparison between treatment mean 1 and treatment mean 4 by computing a Tukey 95 percent simultaneous confidence interval.

Q: Consider the following calculations for a one-way analysis of variance from a completely randomized design with 20 total observations. The response variable is sales in millions of dollars, and the four treatment levels represent the four regions that the company serves. Perform a pairwise comparison between treatment mean 3 and treatment mean 4 by computing a Tukey 90 percent simultaneous confidence interval.

Q: Consider the following calculations for a one-way analysis of variance from a completely randomized design with 20 total observations. Compute a 95 percent confidence interval for the second treatment mean.

Q: BlockTreatment 1 2 3 4 Treatment MeanTr1 2 1 2 3 2Tr2 4 4 1 1 2.5Tr3 3 4 3 2 3Block Mean 2 3 3 2 overall mean = 2.5Consider the randomized block design with 4 blocks and 3 treatments given above. Find the Tukey simultaneous 95 percent confidence interval for the difference between the means of block 2 and block 4.

Q: BlockTreatment 1 2 3 4 Treatment MeanTr1 2 1 2 3 2Tr2 4 4 1 1 2.5Tr3 3 4 3 2 3Block Mean 2 3 3 2 overall mean = 2.5Consider the randomized block design with 4 blocks and 3 treatments given above. Test H0: there is no difference between treatment effects at = .05.

Q: Consider the following one-way ANOVA table. Source df Sum of Squares Model 3 213.88125 Error 20 11.208333 Total 23 225.0895 What is the value of the F statistic?

Q: In a one-way analysis of variance with three treatments, each with five measurements, in which a completely randomized design is used, compute the F statistic where the sum of squares treatment is 17.0493 and the sum of squares error is 8.028.

Q: Find a Tukey simultaneous 95 percent confidence interval for C - B, where C = 51.5, B = 55.8, and MSE = 6.125. There were 4 treatments and 24 observations total, and the number of observations were equal in each group.

Q: Find a Tukey simultaneous 95 percent confidence interval for 1 - 2, where 1 = 33.98, 2 = 36.56, and MSE = 0.669. There were 15 observations total and 3 treatments. Assume that the number of observations in each treatment is equal.

Q: Looking at four different diets, a researcher randomly assigned 20 equally overweight individuals into each of the four diets. What are the degrees of freedom for the individual confidence intervals?

Q: Looking at four different diets, a researcher randomly assigned 20 equally overweight individuals into each of the four diets. What are the degrees of freedom total?

Q: Looking at four different diets, a researcher randomly assigned 20 equally overweight individuals into each of the four diets. What are the degrees of freedom for the error?

Q: Looking at four different diets, a researcher randomly assigned 20 equally overweight individuals into each of the four diets. What are the degrees of freedom for the treatments?

Q: ANOVA table

Q: What is the degrees of freedom error for a randomized block design ANOVA test with 4 treatments and 5 blocks?

Q: What is the degrees of freedom treatment (between-group variation) of a completely randomized design (one-way) ANOVA test with 4 groups and 15 observations per each group?

Q: What is the degrees of freedom error (within-group variation) of a completely randomized design (one-way) ANOVA test with 4 groups and 15 observations per each group?

Q: Consider the following one-way ANOVA table.Source df Sum of SquaresModel 3 213.88125Error 20 11.208333Total 23 225.0895If there are an equal number of observations in each group, then each group (treatment level) consists of how many observations?

Q: Consider the one-way ANOVA table. Source df Sum of Squares Model 3 213.88125 Error 20 11.208333 Total 23 225.0895

Q: Consider the one-way ANOVA table.Source df Sum of SquaresModel 3 213.88125Error 20 11.208333Total 23 225.0895What is the mean square error?

Q: Consider the one-way ANOVA table.Source df Sum of SquaresModel 3 213.88125Error 20 11.208333Total 23 225.0895What is the treatment mean square?

Q: In a one-way analysis of variance with three treatments, each with five measurements, in which a completely randomized design is used, what is the degrees of freedom for error?

Q: In a one-way analysis of variance with three treatments, each with five measurements, in which a completely randomized design is used, what is the degrees of freedom for treatments?

Q: If the total sum of squares in a one-way analysis of variance is 25 and the treatment sum of squares is 17, then what is the error sum of squares?

Q: In general, a Tukey simultaneous 100(1 - ) percent confidence interval is _________ the corresponding individual 100(1 - ) percent confidence interval.A. wider thanB. narrower thanC. no different fromD. two times more than

Q: The variable of interest in an experiment is referred to as the __________ variable. A. categorical B. regression C. response D. factor

Q: The ___________________ units are the entities (objects, people, etc.) to which the treatments are assigned. A. variable B. block C. experimental D. random

Q: In a one way ANOVA table, the ___________ the value of MSE, the higher the probability of rejecting the hypothesis that all treatment means are equal. A. closer to 1 B. closer to 0 C. larger D. smaller

Q: In performing a one-way ANOVA, the _________ is the between-group variance. A. MS Error B. MS Treatment C. SS Error D. SS Treatment

Q: In performing a one-way ANOVA, _________ measures the variability of the observed values around their respective means by summing the squared differences between each observed value of the response and its corresponding treatment mean. A. SS Error B. SS Treatment C. SS Total D. SS Treatment/SS Error

Q: The dependent variable, the variable of interest in an experiment, is also called the ___________ variable. A. categorical B. regression C. response D. factor

Q: In a ___________________ experimental design, independent random samples of experimental units are assigned to the treatments. A. one-way ANOVA B. two-way ANOVA C. randomized block D. balanced complete factorial

Q: In one-way ANOVA, the total sum of squares is equal to _______________________.A. Treatment SS + Error SSB. Treatment SS - Error SSC. Treatment SS Error SSD. Treatment SS/Error SS

Q: A ___________ design is an experimental design that compares v treatments by using d blocks, where each block is used exactly once to measure the effect of each treatment. A. one-way ANOVA B. two-way ANOVA C. randomized block D. balanced complete factorial

Q: The F test for testing the difference between means is equal to the ratio of Mean Square _____________ over Mean Square __________________. A. Treatment, Error B. Error, Treatment C. Treatment, Total D. Error, Total

Q: ___________ refers to applying a treatment to more than one experimental unit.A. RandomizationB. Balanced experimentC. One-way ANOVAD. Replication

Q: ___________ simultaneous confidence intervals test all of the pairwise differences between means, respectively, while controlling the overall Type I error. A. Randomized B. Tukey C. Covariate D. Interacting

Q: ANOVA tableThe Excel/MegaStat output given above summarizes the results of a one-way analysis of variance in an attempt to compare the performance characteristics of four brands of vacuum cleaners. The response variable is the amount of time it takes to clean a specific size room with a specific amount of dirt.At a significance level of .05, the null hypothesis for the ANOVA F test is rejected. Analysis of the Tukey simultaneous confidence intervals shows that at the significance level (experimentwise) of .05, we would conclude thatA. all four brands of vacuum cleaners differ from each other in terms of their performance.B. brand 1 differs from brand 2, and brand 2 differs from brand 3, while the rest of the vacuum cleaner pairs do not differ from each other in terms of their performance.C. brand 1 differs from brand 2, and brand 3 differs from brands 1, 2, and 4, while the rest of the vacuum cleaner pairs do not differ from each other in terms of their performance.D. only brand 3 differs from the other three brands (brands 1, 2, and 3), while the rest of the vacuum cleaner pairs do not differ from each other in terms of their performance.E. none of the four brands of vacuum cleaners differ from each other in terms of their performance.

Q: We have just performed a one-way ANOVA on a given set of data and did not reject the null hypothesis for the ANOVA F test. Assume that we are able to perform a randomized block design ANOVA on the same data. For the randomized block design ANOVA, the null hypothesis for equal treatments will ___________ be rejected. A. always B. sometimes C. never

Q: We have just performed a one-way ANOVA on a given set of data and rejected the null hypothesis for the ANOVA F test. Assume that we are able to perform a randomized block design ANOVA on the same data. For the randomized block design ANOVA, the null hypothesis for equal treatments will __________ be rejected. A. always B. sometimes C. never

Q: Which of the following is not an assumption for one-way analysis of variance? A. The p populations of values of the response variable associated with the treatments have equal variances. B. The samples of experimental units associated with the treatments are randomly selected. C. The experimental units associated with the treatments are independent samples. D. The number of sampled observations must be equal for all p treatments. E. The distribution of the response variable is normal for all treatments.

Q: In the randomized block ANOVA, the sum of squares for factor 1 equalsA. SSTO - SS(error) - SS(interaction).B. SSTO - SS(factor 2) - SSE.C. SSTO - SS(interaction) - SS(factor 2).D. SSTO - SS(factor 2).E. SSTO - SS(error).

Q: In the one-way ANOVA, the treatment sum of squares equalsA. SSTO - SS(error) - SS(interaction).B. SSTO -SS(factor 1) - SSE.C. SSTO - SS(interaction) - SS(factor 1) - SS(factor 2).D. SSTO - SS(factor 1) -SS(factor 2).E. SSTO - SS(error).

Q: When we compute 100(1 - ) confidence intervals, the value of is called theA. comparisonwise error rate.B. Tukey simultaneous error rate.C. experimentwise error rate.D. pairwise error rate.

Q: A sum of squares that measures the variability among the sample means is referred to as the A. treatment sum of squares. B. error sum of squares. C. sum of squares within-treatment. D. total sum of squares. E. interaction sum of squares.

Q: A sum of squares that measures the total amount of variability in the observed values of the response variable is referred to as the A. treatment sum of squares. B. error sum of squares. C. sum of squares within-treatment. D. total sum of squares. E. interaction sum of squares.

Q: The advantage of the randomized block design over the completely randomized design is that we are comparing the treatments by using ________ experimental units. A. randomly selected B. the same C. different D. representative E. equally timed

Q: After analyzing a data set using the one-way ANOVA model, the same data are analyzed using the randomized block design ANOVA model. SS (Treatment) in the one-way ANOVA model is _______________ the SS (Treatment) in the randomized block design ANOVA model. A. always equal to B. always greater than C. always less than D. sometimes greater than

Q: Which one of the following is not an assumption of one-way analysis of variance? A. random selection of samples from each population B. equality of the population variances C. equality of the population means D. Samples selected from each treatment population all have normal distributions.

Q: In a completely randomized (one-way) analysis of variance problem with c groups and a total of n observations in all groups, the variance between groups is equal toA. (Total sum of squares) - (Sum of squares within columns).B. (Sum of squares between columns)/(c - 1).C. (Total sum of squares) - [(Sum of squares within columns)/(n - c)].D. [(Total sum of squares)/(n - 1)] - [(Sum of squares between columns)/(c - 1)].

Q: In a completely randomized ANOVA, with other things equal, as the sample means get closer to each other, the probability of rejecting the null hypothesis A. decreases. B. increases. C. is unaffected.

Q: When using a completely randomized design (one-way analysis of variance), the calculated F statistic will decrease as A. the variability among the groups decreases relative to the variability within the groups. B. the total variability increases. C. the total variability decreases. D. the variability among the groups increases relative to the variability within the groups.

Q: When computing a confidence interval for the difference between two means, the width of the (1 - ) confidence interval based on the Tukey procedure will be __________ the width of the (1 - ) individual confidence interval based on the t statistic.A. greater thanB. less thanC. the same asD. sometimes greater than, sometimes less than

Q: When computing confidence intervals using the Tukey procedure, for all possible pairwise comparisons of means, the experimentwise error rate will beA. equal to .B. less than .C. greater than .

Q: When computing individual confidence intervals using the t statistic, for all possible pairwise comparisons of means, the experimentwise error rate will beA. equal to ..B. less than .C. greater than .

Q: Different levels of a factor are called ____________. A. treatments B. variables C. responses D. observations

Q: In a 2-way ANOVA, if factor 1 has a levels and factor 2 has b levels, then there are a total of _______ treatments.A. a + bB. a bC. |a - b|D. a/bE. a

Q: The ANOVA procedure for a two-factor factorial experiment partitions the total sum of squares into three components, SS first factor, SS second factor, and SSE.

Q: In a 2-way ANOVA, treatment is considered to be a combination of a level of factor 1 and a level of factor 2.

Q: If sample mean plots look essentially parallel, we can intuitively conclude that there is an interaction between the two factors.

Q: Interaction exists between two factors if the relationship between the mean response and one factor depends on the other factor.

Q: In one-way ANOVA, as the between-treatment variation decreases, the probability of rejecting the null hypothesis increases.

Q: In one-way ANOVA, the numerator of the F statistic is an estimate of the population variance based on within-treatment variation.

Q: In one-way ANOVA, other factors being equal, the further apart the treatment means are from each other, the more likely we are to reject the null hypothesis associated with the ANOVA F test.

Q: In one-way ANOVA, the numerator degrees of freedom equals the number of samples being compared.

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