Hypothesis test with t – Exercise 1 Step 1: State the hypotheses H 0 :  = 50H 1 = 50 Step 2: Locate critical region 2 tail test,  =.05, df = =24 t critical = Step 3: Compute test statistic t = (M –  )/s M s M = s/ = 6/5 = 1.2 = (54 – 50)/1.2 = 3.33 Step 4: Make a decision Since the t statistic for our mean is in the critical region (3.33 > 2.064), we reject H 0 and conclude that there is a significant treatment effect.

Hypothesis test with t – Exercise 2a Step 1: State the hypotheses H 0 :  = 90H 1 = 90 Step 2: Locate critical region 2 tail test,  =.05, df = =24 t critical = Step 3: Compute test statistic t = (M –  )/s M s M = s/ = 5/5 = 1 = (92 – 90)/1 = 2.00 Step 4: Make a decision Since the t statistic for our mean is outside the critical region (2.00 < 2.064), we failed to reject H 0 and conclude that there is no significant treatment effect. Effect size: Cohen’s d = mean difference/standard deviation = 2/5 = 0.40 r 2 = t 2 /(t 2 + df) = 2 2 /( ) = 4/28 = or 14.3%

Hypothesis test with t – Exercise 2b Step 1: State the hypotheses H 0 :  = 90H 1 = 90 Step 2: Locate critical region 2 tail test,  =.05, df = =99 t critical = (use df =60 in table) Step 3: Compute test statistic t = (M –  )/s M s M = = = 0.50 = (92 – 90)/0.50 = 4.00 Step 4: Make a decision Since the t statistic for our mean is in the critical region (4.00 > 2.00), we reject H 0 and conclude that there is a significant treatment effect. Effect size: Cohen’s d = mean difference/standard deviation = 2/5 = 0.40 r 2 = t 2 /(t 2 + df) = 4 2 /( ) = 16/115 = or 13.9%

Hypothesis test with t – Exercise 2c Increasing the sample size (n) changed the outcome of the hypothesis test: With n =25, the 2-point difference was not significant. With n = 100, the 2-point difference was significant. Measures of effect size were relatively unaffected by increasing n: Cohen’s d = 0.40 no matter how many scores are in the sample r 2 only changed slightly (.143 for n =25 and.139 for n = 100) In general, effect size is not significantly affected by sample size.