Question

As the sample size for a t-distribution increases, the differences between the t-distribution and the standard normal distribution ______.

Answer 1

Answer:

The differences become smaller

Step-by-step explanation:

Normally, we use the t-distribution table rather than the normal distribution when the population standard deviation is unknown and when the sample size is small i.e. less than 30.

Now, as the sample size gets bigger, we will be getting closer to the point where we have to use the normal distribution.

This means that as the sample size increases, the values of the t-distribution will be getting close to that of the normal distribution because normal distribution is used when sample is more than 30.

For example the t-value for a sample of 25 people would be closer to the normal distribution value for a sample of 35 people while a t-value for a sample of 15 people will be far away from the normal distribution value for a sample of 35 people.

Thus, as the sample size increases, the differences between the t-distribution and standard normal distribution becomes smaller.