Question

Easier Professor - Significance Test (Raw Data, Software Required):
Next term, there are two sections of STAT 260 - Research Methods being offered. One is taught by Professor Smith and the other by Professor Jones. Last term, the class average from Professor Smith's section was higher. You want to test whether or not this difference is significant. A significant difference is one that is not likely to be a result of random variation. The scores from last year's classes are given in the table below. Test the claim that the average from Professor Smith's section was significantly different from Professor Jones' section. Use a 0.05 significance level.

(a) The claim states there is a significant difference in means (μ₁ − μ₂ ≠ 0). What type of test is this?

This is a left-tailed test.

This is a two-tailed test.    

This is a right-tailed test.

(b) Use software to calculate the test statistic. Do not 'pool' the variance. This means you do not assume equal variances.
Round your answer to 2 decimal places.

t =

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.
P-value =

(d) What is the conclusion regarding the null hypothesis?

reject H₀

fail to reject H₀    

(e) Choose the appropriate concluding statement.

The data supports the claim that the average from Professor Smith's section was significantly different from Professor Jones' section.

While the average from Professor Smith's section was higher than Professor Jones', the difference was not great enough to be considered significant.     

We have proven that Professor Smith is the easier professor.

We have proven there was no difference between the averages from the two different professors.

    

    

Prof Smith (x1)	Prof Jones (x2)
48	40
69	62
55	49
86	80
89	81
87	81
96	89
73	67
76	69
72	64
83	76
77	71
88	82
89	81
72	66
79	71
81	73
75	67
98	90
88	81
68	61
63	56
80
79
100
86
93
71

Answer 1

This problem has been solved using excel

Go to Data, select Data Analysis, select t-test: t-Test: Two-Sample Assuming Unequal Variances

H0: μ1 − μ2 = 0

H1: μ1 − μ2 ≠ 0

t-Test: Two-Sample Assuming Unequal Variances
	Prof Smith (x1)	Prof Jones (x2)
Mean	79.32142857	70.77272727
Variance	150.744709	155.9935065
Observations	28	22
Hypothesized Mean Difference	0
df	45
t Stat	2.420422149
P(T<=t) one-tail	0.009800753
t Critical one-tail	1.679427393
P(T<=t) two-tail	0.019601506
t Critical two-tail	2.014103389

Since p-value (0.0196) is less than 0.05, we reject the null hypothesis and conclude that μ1 − μ2 ≠ 0. So there is a significant difference in means.

a) Two-taild test

b) t = 2.42

c) Reject H0

d) The data supports the claim that the average from Professor Smith's section was significantly different from Professor Jones' section.