Question

In general, the greater the sample size (n) is, the ___________ the degrees of freedom (n − 1) are, and the better the t distribution approximates the normal distribution

Answer 1

The greater the sample size (n) is, the larger the degrees of freedom (n − 1) are, and the better the t distribution approximates the normal distribution.

Step-by-step explanation:

The greater the sample size (n) is, the larger the degrees of freedom (n − 1) are, and the better the t distribution approximates the normal distribution.

The t-distribution approaches the standard normal distribution as the sample size gets larger. This is because the t-distribution is a family of distributions, and as the degrees of freedom (n − 1) increase, the shape of the t-distribution becomes more like the standard normal distribution.

For example, if we have a large sample size of 1000, the t distribution with 999 degrees of freedom will closely resemble the standard normal distribution.