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 (μ_{1} − μ_{2} ≠ 0). What type of test is this? This is a lefttailed test. This is a twotailed test. This is a righttailed 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 Pvalue of the test statistic. Round to 4 decimal places. Pvalue = (d) What is the conclusion regarding the null hypothesis? reject H_{0} fail to reject H_{0} (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. 

This problem has been solved using excel
Go to Data, select Data Analysis, select ttest: tTest: TwoSample Assuming Unequal Variances
H0: μ1 − μ2 = 0
H1: μ1 − μ2 ≠ 0
tTest: TwoSample 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) onetail  0.009800753  
t Critical onetail  1.679427393  
P(T<=t) twotail  0.019601506  
t Critical twotail  2.014103389 
Since pvalue (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) Twotaild 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.
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