Refer to the previous exercise. To avoid bias from the samples being unbalanced with such small n, the psychologist redesigned the experiment. She forms three pairs of subjects, such that the patients matched in any given pair are similar in health and socioeconomic status.

For each pair, she randomly selects one subject for each therapy. Table 7.22 shows the improvement scores, and Table 7.23 shows some results of using SPSS to analyze the data.

(a) Compare the means by (i) finding the difference of the sample means for the two therapies, (ii) finding the mean of the difference scores. Compare.

(b) Verify the standard deviation of the differences and standard error for the mean difference.

(c) Verify the confidence interval shown for the population mean difference. Interpret.

(d) Verify the test statistic, df, and P-value for comparing the means. Interpret.

TABLE 7.22 Pair Therapy A Therapy B 1 10 30 2 20 45 3 30 45 TABLE 7.23 Paired Samples Statistics Variable Mean N Std. Dev. Std. Error Therapy A 20.00 3 10.000 5.774 Therapy B 40.00 3 8.660 5.000 Paired Samples Test Std. Error Sig.

Mean Std. Dev. Mean t df (2-tailed)

Yes - No 20.00 5.00 2.887 6.93 2 .020