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 0.01 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 two-tailed test. This is a left-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 41 69 63 55 49 86 80 89 82 87 81 96 88 73 66 76 70 72 65 83 75 77 70 88 82 89 83 72 64 79 73 81 74 75 68 98 92 88 80 68 60 63 55 80 79 100 86 93 71

Answer 1

The statistical software output for this problem is:

Two sample T hypothesis test: Hi : Mean of Prof Smith (x1) 2 : Mean of Prof Jones (x2) 1 - P2 : Difference between two means Ho : 1 - 2 = 0 HA: P1 - H270 (without pooled variances) Hypothesis test results: Difference Sample Diff. Std. Err. DF T-Stat P-value P1 - 2 8.3668831 3.5554489 44.616442 2.3532565 0.0231

Hence,

a) Two - tailed test

b) t = 2.35

c) P - value = 0.0231

d) Reject Ho

e) While the average from Professor Smith's section was higher than Professor Jones', the difference was not great enough to be considered significant. Option B is correct.