A social psychologist is interested in understanding how the use of anti- depres

Question

A social psychologist is interested in understanding how the use of anti- depressants affects an individual’s social life. He creates a scale where a score of 10 equals “highly social” and 1 indicates “highly unsocial.” The psychologist then asks his subjects several questions before beginning anti-depressants and again after they have been taking them for three months.   

a) What is the null hypothesis?

b) If a research obtains a t-score of -2.93, should they retain or reject the null hypothesis?

c) If the calculated z-score is 1.24, should we retain or reject the null hypothesis?

d) What do these results tell us about anit-depressants and sociability?

Explanation / Answer

Let M = Average score on the sociality scale created by the psychologist Let Mo = Average score on the sociality scale before giving the anti-depressant Let Mn = Average score on the sociality scale after giving the anti-depressant a) Null and alternate hypothesis are Ho : Mn = Mo (Use of anti depressants does not affect the sociality scale of an individual) Ha : Mn Mo b) t-score = -2.93 We consider = 0.05 Note that the sample size is not given From the t distribution table, we find that for degrees of freedom = 4 We assume sample size is >= 5 but less than 30 since t-score is used Hence if the sample size is >= 5 but less than 30, reject the null hypothesis c) Z-score = 1.24 We consider = 0.05 Since this is a two tailed test, from the standard normal tables, the two-tailed P value for z-score 1.24 equals 0.2150 0.2150 > 0.05 Hence we do not reject the null hypothesis for z-score 1.24 d) The results obtained from t-score and z-score both together are inconclusive. It is important to know the sample size and the level of significance If sample size is high we will use z-score indicating that there is no significant effect of the anti-depressant on the social life If sample size is small we will use t-score indicating that there is a significant effect of the anti-depressant on the social life

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