How to perform a t-test?

To perform a t-test, first determine the null and alternative hypotheses. Then calculate the t-value and compare it to the critical value.

A t-test is a statistical test used to determine if there is a significant difference between the means of two groups. Before performing a t-test, it is important to determine the null and alternative hypotheses. The null hypothesis states that there is no significant difference between the means of the two groups, while the alternative hypothesis states that there is a significant difference.

To calculate the t-value, first calculate the difference between the means of the two groups. Then, calculate the standard error of the difference between the means. This can be done using the following formula:

SE = sqrt((s1^2/n1) + (s2^2/n2))

Where s1 and s2 are the standard deviations of the two groups, and n1 and n2 are the sample sizes of the two groups.

Once the standard error is calculated, the t-value can be calculated using the following formula:

t = (x1 - x2) / SE

Where x1 and x2 are the means of the two groups.

Finally, compare the t-value to the critical value. The critical value can be found using a t-distribution table, with the degrees of freedom equal to the sum of the sample sizes minus two. If the t-value is greater than the critical value, then the null hypothesis can be rejected and it can be concluded that there is a significant difference between the means of the two groups.