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# Answer to Question #3727 in Statistics and Probability for tami

Question #3727
Do a two sample t test. Assume that this is a two sided test with alpha 5%. &lt;br&gt;Find the test stat, p-value and make a decision about the null.
1
2018-07-30T09:23:07-0400
Null hypothesis is that the difference between the two groups is 0.
Alternative hypothesis - the difference between two means is not zero.

Test statistics can be found by the formula

where x1, x2 - are the means of two samples, SD1,2 - standard deviations , n1,2 - the number of observations of two samples respectively.
Then you have to calculate the number of degrees of freedom:

$d.f. = \frac{(SD_1^2/n_1 + SD^2_2 /n_2)^2}{(SD^2_1/n_1)^2/(n_1 -1) + (SD^2_2/n_2)^2/(n_2 -1)}$
and find p-value from the tables (or using t to p value calculator).
If p-value is more than 0.1 (performing two-sided test you must use doubled alpha), we do not reject the null hypothesis; otherwise - we reject it.

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