Question

A college physics professor thinks that two of her sections scored differently on the final exam.  

She collects the scores for the two classes and stores them in a file.

We do not know anything about the test score distributions.

Answer the following. Use alpha = 0.05.

a). What is the value of the test statistic?

b). What is the p-value?

c). Is she correct in stating that the final exam scores from the two sections are not equal to each other?

Here are the score sets

Set 1: 74, 79, 65, 58, 67, 61, 63, 64, 62, 72, 66, 58, 66, 63, 61, 73, 77, 68, 62, 67, 81, 80, 58

Set 2: 75, 77, 76, 82, 88, 91, 92, 70, 89, 85, 71, 82, 91, 77, 67, 87, 92, 88, 94, 85, 97, 93, 74

Answer 1

The data provided is:

	Set 1	Set 2
	74	75
	79	77
	65	76
	58	82
	67	88
	61	91
	63	92
	64	70
	62	89
	72	85
	66	71
	58	82
	66	91
	63	77
	61	67
	73	87
	77	92
	68	88
	62	94
	67	85
	81	97
	80	93
	58	74
Count	23	23
Average	67.17391	83.6087
St. Dev	7.170978	8.648379

The following null and alternative hypotheses need to be tested:

Ho: μ1​ = μ2​

Ha: μ1​ ≠ μ2​

a)

Test Statistics

Since it is assumed that the population variances are equal, the t-statistic is computed as follows:

b)

The p-value is

c)

Since it is observed that ∣t∣=7.016>tc​=2.015, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0, and since p=0<0.05, it is concluded that the null hypothesis is rejected. Therefore, there is enough evidence to claim that the population mean μ1​ is different than μ2​, at the 0.05 significance level. Hence the teacher is correct in stating that the final exam scores from the two sections are not equal to each other.

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