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Answer on Statistics and Probability Question for tami

Question #3727
Do a two sample t test. Assume that this is a two sided test with alpha 5%. <br>Find the test stat, p-value and make a decision about the null.
Expert's answer
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

/cgi-bin/mimetex.cgi?%5Cfrac%7B%5Cbar%7Bx_1%7D%20-%20%5Cbar%7Bx_2%7D%7D%7B%5Csqrt%7B%5Cfrac%7BSD_1%5E2%7D%7Bn_1%7D+%20%5Cfrac%7BSD_2%5E2%7D%7Bn_2%7D%7D%7D
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:

http://latex.codecogs.com/gif.latex?d.f.%20=%20%5Cfrac%7B%28SD_1%5E2/n_1%20+%20SD%5E2_2%20/n_2%29%5E2%7D%7B%28SD%5E2_1/n_1%29%5E2/%28n_1%20-1%29%20+%20%28SD%5E2_2/n_2%29%5E2/%28n_2%20-1%29%7D
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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