1.If the null hypothesis in a t-test for two samples is not rejected, what conclusion can be drawn about the two means of the categorical variable?
2. . Assume you collected larger samples of individuals to test your null hypothesis in question #1. Specifically, the sample sizes increased to 200 subjects in each group. Do your results and conclusions change from the test of the smaller sample sizes? (You must show your work).
Ans.
(1). In a t test for two samples, if the null hypothesis is not reject then we conclude that, there is no significant difference between samples i.e. both the samples are drawn from same normal population or they have same means.
(2). In case of large samples, we use normal approximation distribution, but the conclusions are same as for small sample test.
In a large sample test the only difference is use the normal approximation for any type test statistic but the conclusions are same for both types of test.
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