Question

What is a t-score?

Answer 1

Hint: T-distribution, also known as student’s t-distribution, is a statistical methodology of evaluating or calculating the mean of a normally distributed data set. The t-score method of analyzing distribution was first proposed by W.S. Gosset and its main purpose was to either select or reject a null hypothesis.

Complete step by step solution:
A t-score is used when we have a smaller sample (a sample size of approximately less than 30) to analyze and population standard deviation is unknown. Just like z-scores, these are also a type of conversion of individual scores into a standard form of data. These are generally used when the variance or the standard deviation is unknown, so it is used to calculate the probabilities with the sample mean.
The formula for calculating the t-score of a distribution is given by:
$\Rightarrow t=\dfrac{\left( {{x}_{i}}-\mu \right)}{\left( \dfrac{s}{\sqrt{N}} \right)}$
Where,
‘t’ is the required t-score of a distribution.
‘$\overline{x}$’ is the mean of the sample.
‘$\mu $’ is the mean of the population.
‘s’ is the calculated or given standard deviation of the sample. And,
‘N’ is the sample size (generally greater than 20 but less than 30).
Thus, we can use this formula to simply calculate the t-score of a sample distribution.
Hence, a t-score has been properly defined.

Note: The shape of the t-distribution is dependent on the sample size and the range of a t-distribution could range from infinity to infinity. Also, if we compare a normal distribution to a t-distribution, t-distribution is less peaked at the center and more elevated on either side. The standard deviation of a t-distribution should be greater than 1 and the area under a t-distribution is considered to be 1.