Easier Professor - Significance Test: Next term, there are two sections of STAT

Question

Easier Professor - Significance Test: 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. Somehow, you have the relevant data from last term. The results are summarized in the table below where the

x

's are actually population means but we treat them like sample means.

Necessary information:

The Test: 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 (1 2 0). What type of test is this?

This is a right-tailed test.

This is a left-tailed test.

   This is a two-tailed test.

(b) Calculate the test statistic using software or the formula belowt =

where is the hypothesized difference in means from the null hypothesis. 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.

Professor n x s2 s Smith (x1) 21 85.4 127.0 11.27 Jones (x2) 29 77.2 92.9 9.64

Explanation / Answer

The statistical software output for this problem is:

Two sample T hypothesis test:
1 : Mean of Population 1
2 : Mean of Population 2
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 0
(without pooled variances)

Hypothesis test results:

a) This is a two - tailed test.

b) t = 2.70

c) p - value = 0.0103

d) p - value is less than 0.05, so reject the null hypothesis.

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

Option A is correct.

Difference Sample Diff. Std. Err. DF T-Stat P-value 1 - 2 8.2 3.0418255 38.989334 2.6957497 0.0103

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