7. A researcher is interested in whether a certain hour-long film that portrays

Question

7. A researcher is interested in whether a certain hour-long film that portrays the insidious effects of racial prejudice will affect attitudes toward a minority group. Two groups of 31 subjects each were randomly selected and randomly assigned to one of two conditions: Group A watched the movie, and Group B spent the hour playing cards. Both groups were then given a racial-attitude test, wherein high scores represented a higher level of prejudice. The data are as follows: Group A: N= 31; M = 39.62 Group B: N=31; M = 42.60 The estimated standard error of difference between the means was 1.360. a. Test the null hypothesis at the .05 level.

Explanation / Answer

Null hypothesis: M1 - M2 = 0 that is, the difference in the means of the two groups is 0.
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.
For this analysis, the significance level is 0.05. Significance level for two-tailed t-test = 0.05 / 2 = 0.025

Using sample data, we will conduct a two-sample t-test of the null hypothesis.

Standard error, SE = 1.360
Degree of freedom = n-1 = 31 - 1 = 30
t statistic is given by, t = [ (M1 - M2)] / SE = (39.62-42.60)/1.360 = -2.19
We use the t Distribution Chart to find P(t <= -2.19) where degree of freedom is 30.
We get p-value as P(t <= -2.19) = 0.0182.
Since the P-value (0.0182) is less than the significance level (0.025), we can reject the null hypothesis.

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