# T–test

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## Definition: T–test

The t-test is a statistical test of whether two sample means (averages) or proportions are equal. T –tests are particularly useful when the variance of the population is unknown and sample size is small.

A t-test helps you to compare whether two groups have different average values. For example, do men and women have different average heights or not?

There are basic three underlying assumptions before carrying out t-test.

• Each group is considered to be a sample from a distinct population
• the responses in each group are independent of those in the other group
• the distributions of the variable of interest are normal

The test statistic in the t-test is known as the t-statistic.

There is also One Sample t-Test which can be used to compare one group’s average value to a single number. For example, do students of particular college on an average spend Rs 500 on travelling?

Test statistic for one sample t –test

Let x1, x2, ..., xn is a random sample drawn from a normal population with unknown variance σ2.  Using sample data, we can conduct a one-sample t-test.

Calculate, t Test statistic

t=(X-µ)/s/√n

This t – statistic is compared with critical values obtained from t distribution table and the decision to accept/reject hypothesis can be made.

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