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First, examine the two sample t-test (independent groups) example in lecture 6 (the coal mine example), slide 108.

Then, revisit the Matched Pairs (correlated groups) example regarding the safety program in lecture 6, slide 91.

Instead of handling the safety programexampleas a Matched Pairs example as it really should be handled, analyze it as a two-sample t-test of Before Program vs. After Program, ie analyze it with the same process as the coal mining problem.

Please state:

1) the Ho and ha

2) the test statistics & Critical value

3) your conclusion

4) Discuss the results vs. the Matched Pairs results

Slide 108

Most cases, the null hypothesis is set to: Ho : H=o HA : H >O Where u = "the true mean difference" . Then, apply the one-sample t-test! Since the test statistic (2.29) is greater than the critical value (1.796), we REJECT the null hypothesis. We DO have statistically significant evidence to conclude that the null hypothesis is false (at the 0.05 significance level). That is, the TRUE mean is GREATER than 0. There was a significant MORE accidents before the safety program was installed.. The following random samples are measurements of the heat-producing capacity (in millions of calories per ton) of specimens of coal from two mines: Mine 1 8380 8180 8500 7840 7990 Mine 2 7660 7510 7910 8070 7790 . Use the significance level of 0.05 to test whether the means are different. Since the test statistic (2.51) is LESS than the critical value (2.776), we FAIL TO REJECT the null hypothesis. We do NOT have statistically significant evidence to conclude that the null hypothesis is false (at the 0.05 significance level). There is NO evidence to conclude that the two mines differ in terms of the heat producing capacity of their coal. As far as we can tell, the mines are about the same