Question

Which one of the following is a correct statement about the probability distribution of a t random variable?

	a.	The mean is zero but the standard deviation is greater than 1.
	b.	The mean and standard deviation can be any number.
	c.	The mean is zero but the standard deviation is less than 1.
	d.	The mean is zero and the standard deviation is 1.

Answer 1

But sample sizes are sometimes small, and often we do not know the standard deviation of the population. When either of these problems occur, statisticians rely on the distribution of the t statistic(also known as the t score), whose values are given by:

t = [ x - μ ] / [ s / sqrt( n ) ]

where x is the sample mean, μ is the population mean, s is the standard deviation of the sample, and n is the sample size. The distribution of the t statistic is called the t distribution or the Student t distribution.

Ans: The mean and standard deviation can be any number.