Exam 11: Experimental Design and Analysis of Variance

Suppose you are a researcher investigating the annual sales differences among five categories of businesses.Looking at a total of 55 companies equally divided among categories groups A,B,C,D,and

The variable of interest in an experiment is referred to as the __________ variable.

A sum of squares that measures the variability among the sample means is referred to as:

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

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.

Consider the following partial analysis of variance table from a randomized block design with 10 blocks and 6 treatments. What is the treatment mean square?

Consider the randomized block design with 4 blocks and 3 treatments given above. Find Tukey's simultaneous 95 percent confidence interval for the difference between the means of block 2 and block 4.

The 95% individual confidence interval for (treatment mean 1 - treatment mean 2)will always be smaller than the Tukey's 95% simultaneous confidence interval for .

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 degree of freedom for treatments?

Consider the following partial analysis of variance table from a randomized block design with 10 blocks and 6 treatments. Determine the degrees of freedom for error.

Consider the randomized block design with 4 blocks and 3 treatments given above. What is the block mean square?

A researcher has used a one-way analysis of variance model to test whether the average starting salaries differ among the recent graduates from nursing,engineering,business and education disciplines.She has randomly selected four graduates from each of the four areas. If MSE = 4,and SSTO = 120 complete the following ANOVA table.Is there a significant difference in the starting salaries among the four disciplines?

The Excel/Mega-Stat 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. Use the information above and determine an individual 95% confidence interval for .The mean and sample sizes for brand 1 and brand 2 are as follows: ₁ = 2.95, ₂ = 2.28,n₁ = 4 and n₂ = 5.

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

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.

Consider the following partial analysis of variance table from a randomized block design with 10 blocks and 6 treatments. Determine the degrees of freedom for treatments.

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.

The Excel/Mega-Stat 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's simultaneous confidence intervals shows that at the significance level (experimentwise)of .05 we would conclude that

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.

The advantage of the randomized block design over the completely randomized design is that we are comparing the treatments by using ________ experimental units.