There are two sections of statistics, one in the morning (AM) with 24 students and one in the afternoon (PM) with 27 students. Each section takes an identical test. The PM section, on average, scored higher than the AM section. The results are summarized in the table below.
Necessary information:
n  x  s^{2}  s  
PM (x_{1})  27  80.8  277.5  16.66 
AM (x_{2})  24  70.9  250.3  15.82 
The Test: Test the claim that the PM section did significantly better than the AM section, i.e., is the difference in mean scores large enough to believe that something more than random variation produced this difference. Use a 0.05 significance level.
(a) Calculate the test statistic using software or the formula below
t =
(x_{1} − x_{2}) − δ  

where δ is the hypothesized difference in means from the null hypothesis. Round your answer to 2 decimal places.
t =
To account for hand calculations vs software, your answer must be within 0.01 of the true answer.
(b) Use software to get the Pvalue of the test statistic. Round to 4 decimal places. Pvalue =
(c) What is the conclusion regarding the null hypothesis?
reject H_{0}
fail to reject H_{0}
(d) Choose the appropriate concluding statement.
The difference in mean scores is large enough to suggest this difference is due to something more than random variation.
There is not a big enough difference in mean scores to suggest that this difference is anything more than a result of random variation.
We have proven that students in PM sections of statistics do better, on average, than students taking AM sections.
We have proven that there is no difference between AM and PM sections of statistics.