Final answer:
The null hypothesis for a 2 sample t-test states that the means of the two groups being compared are equal, while the alternative hypothesis states that the means of the two groups are not equal.
Step-by-step explanation:
In the context of a 2 sample t-test, the null hypothesis (denoted as H0) states that there is no difference in the means of the two populations from which the two samples were drawn. In symbols, this can be written as H0: μ1 = μ2, where μ1 and μ2 are the population means of the first and second groups, respectively.
On the other hand, the alternative hypothesis (denoted as Ha) suggests that there is a difference between the two population means. In symbols, it is represented as Ha: μ1 ≠ μ2 for a two-tailed test, Ha: μ1 > μ2 for a right-tailed test, or Ha: μ1 < μ2 for a left-tailed test. The type of test (right-, left-, or two-tailed) is determined based on the research question or the direction of the hypothesis.
The choice between a right-tailed, left-tailed, or two-tailed test depends on the specific hypothesis being tested. A right-tailed test is used when the alternative hypothesis suggests that the first population mean is greater than the second; a left-tailed test is appropriate when the alternative suggests the first mean is less than the second.
When conducting a 2 sample t-test, the Student's t-distribution is used instead of the normal distribution because of small sample sizes or unknown population standard deviations, which make the t-distribution a better choice due to its ability to account for this additional uncertainty.