List the properties of Student t-distribution, and discuss how it's similar in comparison to the z-normal...

List the properties of Student t-distribution, and discuss how it's similar in comparison to the z-normal distribution.

Expert Solution

The student t test distribution is applied to estimate the parameters of population when the sample size is small and the standard deviation is not known.

Properties of t test:

1. The shape of t distribution curve is bell shaped and it is symmetrical with mean zero.

2. It ranges from minus infinity to plus infinity.

3. The shape of the distribution undergoes changes depending on the basis of the degree of freedom.

4. It has a platykurtic shape as it is peaked less at the center and higher at the tails.

5. T distribution assumes the character of a normal distribution when the sample size increases. For t distribution the large sample is when n is greater than or equal to 30.

6. The variance of t test is always greater than one.

Similarities :

Both t test and z test are used to test hypothesis. Both these test require data that follow a normal distribution. A normally distributed data means that the data of the sample has an evenly distributed mean which has a curve which is bell shaped.

Rahul Sunny answered 2 years ago

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