# Calculating a test statistic? [closed]

Please help me with this question. I'm pretty sure I know the null hypothesis is that the two means are the same but I'm not sure how to calculate it.

James and Sally looked at sulfide content in seven coal samples. James's results were on average .40 ppm higher than Sally, with a standard deviation of difference being +/- 0.21 ppm. Is the difference between the two significant?

A. Null hypothesis?
B. Calculate test statistic C. Compare with critical values at the 90 and 99% confidence levels. What conclusions can you draw? D. What kind of tests can be carried out with multiple trials of a single sample by each person?

## closed as off-topic by Mithoron, airhuff, Tyberius, Todd Minehardt, TAR86Dec 5 '17 at 6:40

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If you are testing that the results from James and Sally are the same, then you'd reject if James$>$Sally or James$<$Sally so you'd be doing a two-sided test. For 99% confidence this would mean 0.5% James>Sally and 0.5% James$<$Sally.
You already know that the numbers are such that the results have James$>$Sally, so you want to do a one-sided test.
• See Wikipedia article for instance $$t=\dfrac{\bar{X}_{James} - \bar{X}_{Sally}}{s_p/\sqrt{n}}$$ – MaxW Dec 4 '17 at 23:55