Describe about the Sampling Distribution of t.
Describe about the Sampling Distribution of t.
Sampling distribution is used to describe the sample statistic or any function of the sample, which are eventually the functions of sample variates that varies from one sample to another.
Mostly if the sample mean follows a distribution is known to the distribution of the sample.
Sampling distribution of t is also known as student's t distribution. The student's t distribution helps to define the deviation of sample mean from its population mean which are expressed in terms of error, in which the population standard deviation is unknown and the population is normally distributed.
Yet, the student's t test is extended by Prof. R. A. Fisher, it is first released by W. S. Gosset in a publishing paper. According to R. A . Fisher, t distribution is the ratio of normal variate which has mean 0 and variance 1.
Let be a random sample taken from the population which follows normal distribution with known mean and unknown standard deviation . The test statistic is defined as
with degree of freedom
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