Problem 17E

Consider dot plots 1 and 2 shown below. Assume that the two samples represent independent, random samples corresponding to two treatments in a completely randomized design.

a. In which plot is the difference between the sample means small relative to the variability within the sample observations? Justify your answer.

b. Calculate the treatment means (i.e., the means of samples 1 and 2) for both dot plots.

c. Use the means to calculate the Sum of Squares for Treatments (SST) for each dot plot.

d. Calculate the sample variance for each sample and use these values to obtain the Sum of Squares for Error (SSE) for each dot plot.

e. Calculate the Total Sum of Squares [SS(Total)] for the two dot plots by adding the Sums of Squares for Treatments and Error. What percentage of SS(Total) is accounted for by the treatments—that is, what percentage of the Total Sum of Squares is the Sum of Squares for Treatments—in each case?

f. Convert the Sums of Squares for Treatments and Error to mean squares by dividing each by the appropriate number of degrees of freedom. Calculate the F-ratio of the Mean Square for Treatments (MST) to the Mean Square for Error (MSE) for each dot plot.

g. Use the F-ratios to test the null hypothesis that the two samples are drawn from populations with equal means. Use α = .05.

h. What assumptions must be made about the probability distributions corresponding to the responses for each treatment to ensure the validity of the F-tests conducted in part g?

Problem 17E

Consider dot plots 1 and 2 shown below. Assume that the two samples represent independent, random samples corresponding to two treatments in a completely randomized design.

a. In which plot is the difference between the sample means small relative to the variability within the sample observations? Justify your answer.

b. Calculate the treatment means (i.e., the means of samples 1 and 2) for both dot plots.

c. Use the means to calculate the Sum of Squares for Treatments (SST) for each dot plot.

d. Calculate the sample variance for each sample and use these values to obtain the Sum of Squares for Error (SSE) for each dot plot.

e. Calculate the Total Sum of Squares [SS(Total)] for the two dot plots by adding the Sums of Squares for Treatments and Error. What percentage of SS(Total) is accounted for by the treatments—that is, what percentage of the Total Sum of Squares is the Sum of Squares for Treatments—in each case?

f. Convert the Sums of Squares for Treatments and Error to mean squares by dividing each by the appropriate number of degrees of freedom. Calculate the F-ratio of the Mean Square for Treatments (MST) to the Mean Square for Error (MSE) for each dot plot.

g. Use the F-ratios to test the null hypothesis that the two samples are drawn from populations with equal means. Use ? = .05.

h. What assumptions must be made about the probability distributions corresponding to the responses for each treatment to ensure the validity of the F-tests conducted in part g?

Step-by-step solution

Step 1 of 10

a) Plot#2 is the difference between the sample means small relative to the variability within the sample observations. Because if the samples are depicted in the dot plot, then the difference between the means is small relative to the sampling variability of the samples within the treatments-Two samples. We would be inclined not to reject the null hypothesis of equal population means.