# Students were paired by matching their IQs and grades in previous mathematics courses taken

Students were paired by matching their IQs and grades in previous mathematics courses taken. Group A attended lecture and did homework. Group B watched videotapes and did work on a computer. Test to see if there is a significant difference in final exam scores for 2 groups at the .05 level.

Lecture

95

87

91

85

81

79

74

73

71

69

Tapes

99

91

88

90

87

78

79

81

65

74

Solution: We have paired samples, so we have to use t-test for independent samples. We want to test the following hypotheses:

We need to compute the t-statistics for this 2-tailed test. Before that, we need to test to see if the variances can be considered the same. We use Excel to get

We see that the p-value is 0.387458, which is greater than the significance level, and therefore we cannot reject the null hypothesis of equal variances.

Now we test our main hypothesis assuming that the variances are equal. The t-statistics is found using Excel:

 Lecture Tapes 80.5 83.2 78.5 95.51111111 10 10 87.00555556 0 18 -0.64725479 0.262818216 1.734063062 0.525636432 2.100923666

We observe that the p-value is 0.5256, which is greater than the significance level, which means that we fail to reject the null hypothesis. In other words, we don’t have enough evidence to claim that there is a significant difference in final exam scores for 2 groups at the .05 level

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