Final answer:
In a two-tailed Independent samples t-test, the null hypothesis states that two population means are equal (H0: μ1 = μ2), while the alternative hypothesis asserts that the population means are not equal (Ha: μ1 ≠ μ2). The test is two-tailed, meaning differences in either direction are of interest, and the p-value is split between the two tails of the distribution curve.
Step-by-step explanation:
In an Independent samples t-test (two-tailed), the null and alternative hypotheses are statements about the population means of two independent groups. The null hypothesis (H0) typically states that there is no difference in the population means of the two groups, while the alternative hypothesis (Ha) states that there is a difference, without specifying the direction of the difference.
The hypotheses in words and symbols would be:
Null hypothesis (H0): The population mean of group 1 (μ1) is equal to the population mean of group 2 (μ2), represented as H0: μ1 = μ2.
Alternative hypothesis (Ha): The population mean of group 1 (μ1) is not equal to the population mean of group 2 (μ2), represented as Ha: μ1 ≠ μ2.
Since the alternative hypothesis specifies 'not equal to' (≠), it indicates a two-tailed test. The two tails refer to the possibility of the actual mean of group 1 being either greater than or less than the actual mean of group 2, hence 'two-tailed'.
When calculating the p-value for a two-tailed test, the area of interest is split evenly between the left and right tails of the distribution curve. This means that any extreme values leading to rejection of the null hypothesis could be at either end of the distribution, indicating that the means are significantly different in either direction.