I will look at statistics scores of male and female students and will check whether gender has any effect on statistic score. Since both sample are independent, I will chose an independent-samples t test. I will select significance level of 0.05 for the test.
The independent variable is the gender of the student.
The dependent variable is statistics score of student.
Null hypothesis: Statistics score of male and female students are equal.
Alternative hypothesis: Statistics score of male and female students are not equal.
The summary (hypothetical) of statistics scores for male and female are
Male: Sample Mean = 56, sample standard deviation = 23, n = 25
Female: Sample Mean = 67, sample standard deviation = 21, n = 29
The measure of effect size, as indexed by d, is -.50, thus indicating a moderately strong effect between gender and student statistics scores.
The degrees of freedom are 52 (= 25 + 29 -2).
The critical values are t =+ 2.001 and t = -2.001
Assuming equal variances, the pooled variance is 481.62
Estimated standard error of difference is 5.99.
The t statistic is -1.84 and the p-value is 0.072.
Since, the t statistic -1.84 does not fall in rejection region; therefore, the decision is to not reject the null hypothesis.
The result of the test was not statistically significant, t(52) = -1.84, p = .072. Thus the null hypothesis is not rejected; there is no difference in statistic scores between male and female students. Male students (M = 56, SD = 23) and female students (M = 67, SD = 21) did not perform differently in statistic test.
