Statistical reasoning in Psychology
posted by Lilah .
4. Suppose that previous studies have found that the mean amount of sessions necessary to “cure” depressive patients using a particular therapeutic model is 25 sessions, with a standard deviation (σ) of 4. A new model is introduced, and you want to determine whether the amount of sessions needed to “cure” depressive patients with this new model is significantly lower than 25. You select 40 patients, all of whom receive therapy using the new model. You keep track of the amount of sessions these participants take to become “cured”. The test statistic was 3.90.
If you find that a situation requires testing the null hypothesis using the Normal Curve, you don't need to figure degrees of freedom, so you don't have to do (c) for that problem(s). Also, if you find that a problem(s) require(s) testing the null hypothesis using ANOVA, then you don't have to state whether the test is bilateral or unilateral.
Finally, assume that any information that is not provided is therefore unknown to the researcher. Also, assume that the level of significance (alpha) used by the researcher is 0.05.
For each of the following situations, determine:
a) the null and research hypotheses;
b) the hypothesis test used (normal curve, single sample ttest, dependent samples ttest, independent samples ttest, ANOVA). Also state whether the test is unilateral or bilateral;
c) the degrees of freedom
d) the critical value (cutoff score on the comparison distribution);
e) your sample’s test score;
f) your conclusion on whether to accept or reject the null hypothesis (you must show how the comparison of your cutoff score with your sample’s test score leads to your conclusion).

From your first paragraph, I don't know what test statistics you are using. If Z = 3.9, then it is definitely significant at P = .05.
I don't know what the "following situations" are.
Sorry that I can't help more.