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Exam 13: Experimental Design and Analysis of Variance

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Question 31

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The process of using the same or similar experimental units for all treatments is called

A) factoring.
B) blocking.
C) replicating.
D) partitioning.

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Question 32

Multiple Choice

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Which of the following is not a required assumption for the analysis of variance?

A) The random variable of interest for each population has a normal probability distribution.
B) The variance associated with the random variable must be the same for all populations.
C) At least 2 populations are under consideration.
D) Populations under consideration have equal means.

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Question 33

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In the ANOVA, treatments refer to

The process of allocating the total sum of squares and degrees of freedom to the various components is called

In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations) . Also, the design provided the following information. ​ SSTR = 300 (Sum of Squares Due to Treatments) SST = 800 (Total Sum of Squares) ​ The number of degrees of freedom corresponding to between-treatments is

To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below. ​ ​ The test statistic to test the null hypothesis equals

To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below. ​ The mean square due to error (MSE) equals

In a factorial experiment, if there are x levels of factor A and y levels of factor B, there is a total of​

Consider the following information. ​ SSTR = 6750 H₀: μ₁ = μ₂ = μ₃ = μ₄ =μ₅ SSE = 8000 H_a: At least one mean is different ​ The null hypothesis is to be tested at the 5% level of significance. The null hypothesis

Part of an ANOVA table is shown below. ​ The mean square due to treatments (MSTR) is

Three universities in your state decided to administer the same comprehensive examination to the recipients of MBA degrees from the three institutions. From each institution, MBA recipients were randomly selected and were given the test. The following table shows the scores of the students tested by each university. ​ At α = .01, test to see if there is any significant difference in the average scores of all the students who took the exam from the three universities. (Note that the sample sizes are not equal.) Use both the critical and p-value approaches.

For four populations, the population variances are assumed to be equal. Random samples from each population provide the following data. ​ Using a .05 level of significance, test to see if the means for all four populations are the same.

In an analysis of variance, one estimate of σ² is based upon the differences between the treatment means and the

Consider the following ANOVA table. ​ ​ The test statistic to test the null hypothesis equals

When an analysis of variance is performed on samples drawn from k populations, the mean square due to treatments (MSTR) is

An ANOVA procedure is applied to data obtained from 6 samples where each sample contains 20 observations. The critical value of F occurs with

The required condition for using an ANOVA procedure on data from several populations is that the

Part of an ANOVA table is shown below. ​ The number of degrees of freedom corresponding to between-treatments is

An ANOVA procedure is used for data obtained from five populations. Five samples, each comprised of 25 observations, were taken from the five populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are

In an analysis of variance problem involving 3 treatments and 10 observations per treatment, SSE = 399.6. The MSE for this situation is