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

a. In which dot 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 treatment 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 treatment—in each case?

f. Convert the sums of squares for treatment 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 treatment (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.
Take a = .05.
h. What assumptions must be made about the probability distributions corresponding to the responses for each treatment in order to ensure the validity of the F-tests conducted in part g?
i. Conduct a two-sample t-test (Section 7.2) of the null hypothesis that the two treatment means are equal for each dot plot. Use a = .05 and two-tailed tests. Verify that the F-test and t-test results are equivalent.
j. Complete the following ANOVA table for each of the two dot plots:
Source df SS MS F Treatments Error Total