Answer to Question #3727 in Statistics and Probability for tami

Question

Do a two sample t test. Assume that this is a two sided test with alpha 5%.
Find the test stat, p-value and make a decision about the null.

Answer 1

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, SD_1,2 - standard deviations , n_1,2 - the number of observations of two samples respectively.
Then you have to calculate the number of degrees of freedom:


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.