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## What is paired t test?

Paired t-test is a statistical test used to determine whether the means of two related samples are statistically different from each other. The test is performed by comparing the differences between the two samples against a distribution of differences that would be expected by chance alone.

## Procedure for Performing Paired T-Test

A paired T-test is a statistical test used to compare the means of two paired groups. The test is used when the two groups are matched (or paired) with respect to a characteristic that is of interest. For example, a paired T-test could be used to compare the mean weight of two groups of people who have the same gender and age.

The first step in a paired T-test is to calculate the difference between each pair of observations. This can be done using a simple subtracting equation. For example, if we wanted to compare the weight of two groups of people, we would calculate the difference in weight between each person in the two groups.

Once the differences have been calculated, the next step is to determine the standard error of the difference. This can be done using the following equation:

Standard error of the difference =

The standard error of the difference is a measure of how much the difference between the two groups is likely to vary due to chance.

The next step is to determine the test statistic. This can be done using the following equation:

Test statistic =

The test statistic is a measure of how likely it is that the difference between the two groups is due to chance.

The final step is to determine the p-value. This can be done using the following equation:

P-value =

The p-value is a measure of how likely it

## Hypotheses of a Paired T-Test

A paired t-test is a statistical test used to compare the means of two groups that are related to each other. The groups are usually two different samples of the same population, or two different measurements of the same object. For example, you might use a paired t-test to compare the average IQ scores of two groups of people, or the average weight of two groups of people.

The hypothesis of a paired t-test is that the means of the two groups are equal. This hypothesis is tested by calculating a t-statistic. If the t-statistic is greater than the t-distribution, then the hypothesis is rejected and it is concluded that the means of the two groups are not equal.

## Assumptions of a Paired T-Test

The paired t-test is a statistical test used to determine whether the means of two groups of related data are statistically different from each other. In order to perform a paired t-test, the following assumptions must be met:

The two groups of data must be from the same population.

The two groups of data must be randomly sampled from the population.

The two groups of data must be independent of each other.

The two groups of data must have the same variance.

The two groups of data must have the same number of observations.

## Solved Example

Q. You are given the following data.

x 1 2 3 4

y 1 3 5 7

Find the equation of the line that passes through the points (1, 1) and (4, 7).

The equation of the line that passes through the points (1, 1) and (4, 7) is y = 2x + 1.