How to perform a two-sample t-test?

To perform a two-sample t-test, first calculate the means and standard deviations of both samples.

A two-sample t-test is used to compare the means of two independent samples to determine if they are significantly different from each other. To perform this test, you will need to calculate the means and standard deviations of both samples.

Next, calculate the pooled standard deviation using the formula:

s_p = sqrt(((n1-1)s1^2 + (n2-1)s2^2)/(n1+n2-2))

where s1 and s2 are the standard deviations of the two samples, n1 and n2 are the sample sizes, and s_p is the pooled standard deviation.

Then, calculate the t-statistic using the formula:

t = (x1 - x2) / (s_p * sqrt(1/n1 + 1/n2))

where x1 and x2 are the sample means, n1 and n2 are the sample sizes, and s_p is the pooled standard deviation.

Finally, determine the degrees of freedom using the formula:

df = n1 + n2 - 2

and use a t-distribution table or calculator to find the p-value associated with the t-statistic and degrees of freedom. If the p-value is less than the chosen significance level (usually 0.05), then the means of the two samples are significantly different from each other.