Question

A teacher wants to compare the performance of her morning class versus her afternoon class. The morning class has 6 students and the afternoon class has 6. To keep things fair, both classes were given the exact same test. She is interested in knowing whether the average in the morning class is less than the average in the afternoon class. The test results for each class are given below:

Morning Class	Afternoon Class
32.8	55.5
65.8	61.4
43.7	67.0
63.3	75.4
82.7	64.7
59.8	48.6

What would be the correct hypothesis test for her to use? μ₁ is the mean for the morning class and μ₂ is the mean for the afternoon class.

H₀: μ₁ > μ₂ vs. H_a: μ₁ = μ₂
H₀: μ₁ < μ₂ vs. H_a: μ₁ = μ₂
H₀: μ₁ = μ₂ vs. H_a: μ₁ < μ₂
H₀: μ₁ = μ₂ vs. H_a: μ₁ > μ₂

The teacher is assuming that the standard deviations between the two classes are identical. Calculate the value of s_p² that she should be using.

What is the number of degrees of freedom?

Calculate the test statistic

Assuming a significance level of α = 0.05, do we reject H₀

Yes, we reject H₀
No, we fail to reject H₀

Answer 1

H₀: μ₁ = μ₂ vs. H_a: μ₁ < μ₂

s_p² = 197.5748

The number of degrees of freedom = 10

The test statistic = -0.503

No, we fail to reject H₀

Morning Class	Afternoon Class
58.017	62.100	mean
17.560	9.316	std. dev.
6	6	n
	10	df
	-4.0833	difference (Morning Class - Afternoon Class)
	197.5748	pooled variance
	14.0561	pooled std. dev.
	8.1153	standard error of difference
	0	hypothesized difference
	-0.503	t
	.3129	p-value (one-tailed, lower)

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