As the degrees of freedom for the t-distribution increase, the distribution approaches



the value of zero for the mean.

the t-distribution.

the normal distribution.

the F distribution.

I'm thinking C...

You are correct! (The distribution approaches a normal distribution.)

You are correct! As the degrees of freedom for the t-distribution increase, the distribution approaches the normal distribution. The t-distribution converges to the normal distribution as the degrees of freedom increase, with a mean of zero and a standard deviation of one. So, option C is the correct answer.

You are correct! As the degrees of freedom for the t-distribution increase, the distribution approaches the normal distribution. This is known as the Central Limit Theorem.

The Central Limit Theorem states that as the sample size increases, the sampling distribution of the mean approaches a normal distribution, regardless of the shape of the original population. The t-distribution is very similar to the normal distribution, but has thicker tails to account for the uncertainty due to smaller sample sizes.

To arrive at this answer, you can recall the properties of the t-distribution. The t-distribution is a family of distributions that depend on the degrees of freedom. When the degrees of freedom are small, the t-distribution has more spread and thicker tails compared to a normal distribution. However, as the degrees of freedom increase, the t-distribution becomes closer and closer to the standard normal distribution.

In this case, as the degrees of freedom increase, the t-distribution approaches the normal distribution with zero mean and a standard deviation of 1. Therefore, option C is the correct answer.