Ehat is the formula for calculating t test

Answer 1

The formula for calculating the t-test depends on the specific type of t-test being conducted.

There are three main types of t-tests:

1. One-sample t-test: Used to determine if the mean of a single sample differs significantly from a hypothesized population mean.
Formula: t = (X - μ) / (s /√n)
Where t is the t-score, X is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

2. Independent samples t-test: Used to determine if the means of two independent samples differ significantly from each other.
Formula: t = (X1 - X2) / √[(s1^2 / n1) + (s2^2 / n2)]
Where t is the t-score, X1 and X2 are the means of the two samples, s1 and s2 are the standard deviations of the two samples, and n1 and n2 are the sizes of the two samples.

3. Paired samples t-test: Used to determine if the means of two dependent samples, or paired observations, differ significantly from each other.
Formula: t = (X1 - X2) / (s / √n)
Where t is the t-score, X1 and X2 are the means of the paired observations, s is the standard deviation of the differences between pairs, and n is the number of pairs.

It is important to note that the t-test assumes certain assumptions, such as the data being normally distributed and the variances of the two samples being equal (for independent samples t-test). If these assumptions are not met, alternative statistical tests may be more appropriate.