A team of researchers stated that effective methods of therapy help people access and process their emotions (Watson \& Bedard, 2006). They looked at the level of emotional processing brought about by two different types of therapy for clients diagnosed with depression. The first group \((N=17)\) took part in cognitive-behavioral therapy \((\mathrm{CBT})\). The second group \((N=21)\) took part in process-experiential therapy (PET). The Experiencing Scale measured their level of emotional processing. The CBT group scored a mean of 2.73 on the scale, with a standard deviation of .46. The PET group scored a mean of 3.04, with a standard deviation of .42. Use the steps of hypothesis testing to determine whether one therapeutic technique brings about more emotional processing than the other

a. State the null and alternative hypotheses \(\left(\mathrm{H}_{0}\right.\) and \(\left.\mathrm{H}_{1}\right)\).

b. Make a decision about the null hypothesis.

(1) Calculate the degrees of freedom (df).

(2) Set alpha ( \(\alpha\) ), identify the critical values (draw the distribution), and state a decision rule.

(3) Calculate a value for the \(t\)-test for independent means (when calculating the standard error of the difference \(\left[s_{\bar{X}_{1}}-\bar{X}_{2}\right]\), be sure to use the formula for unequal sample sizes),

(4) Make a decision whether to reject the null hypothesis.

(5) Determine the level of significance.

c. Draw a conclusion from the analysis.

d. Does one of the therapy methods appear to be more effective than the other?