# 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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