Question

What is t-statistic?

Answer 1

Hint: Before getting into the topic t-statistic, we need to know about the t-test. A t-test is a statistical test that is usually used to compare the measured means of two groups that we have taken. A test acts as one of the hypothesis testing tools, which allows testing of our assumption to a population.
Usually, a t-test depends on the t-statistic, the t-distribution (which is similar to normal distribution), and the degrees of freedom to find the statistical significance.
And the term statistic is a quantity that can be obtained finally from a sample of a population. Example for a statistic: In a school, We are taking a sample of \[100\] students out of $1000$ students. And then we are looking at the average height of our sample students. The resulting average is the statistic of our assumed sample.
A t-statistic is commonly used in a t-test to accept or reject the null hypothesis.
Formula used:
\[t - statistic = \dfrac{{\overline x - \mu }}{{\dfrac{s}{{\sqrt n }}}}\]
Where,
\[\overline x \] Denotes the mean of the sample,
$\mu $ Denotes the mean of the population,
$s$ denotes the standard deviation of the sample,
$n$ is the sample size, and
$t$ is t-statistic

Complete step by step answer:
A t-statistic used t-test generally for statistical hypothesis testing. We use t-statistic in the calculation where the sample size $n$ is less than or equal to \[30\]. Also, it allows sample data to test the hypothesis about an unknown population mean. That is, the t-statistic can be used to test the hypothesis about a completely unknown population standard deviation since it only required information about the sample standard deviation.
Follow the below steps to calculate a t-statistic:
1) We need to find the sample mean ($\overline x $ )
2) Then calculate the population ($\mu $ )(both $\overline x $and $\mu $will be given)
3) Now, calculate the standard deviation of the sample ($s$ ). Hence, t-statistic can be the formula,
\[t - statistic = \dfrac{{\overline x - \mu }}{{\dfrac{s}{{\sqrt n }}}}\]

Note:
The t-statistic is used to compare the means of two groups and in case of more than the two groups, we prefer analysis of variance (ANOVA). Generally, we apply the t-statistic in the calculation where the sample size $n$ is less than or equal to \[30\] and used in t-test to accept or reject the null hypothesis.