Question

One can approximate the t statistic using the z score (and substituting s₁² and s₂² for the population variances) if:

a) The sample size is small.
b) The population is normally distributed.
c) The sample variances are equal.
d) The degrees of freedom are known.

Answer 1

The statement that accurately describes when one can approximate the t statistic using the z score is when the population is normally distributed.

Step-by-step explanation:

The statement that accurately describes when one can approximate the t statistic using the z score is:

b) The population is normally distributed.

The t statistic is used when the population is not normally distributed or when the population standard deviation is unknown. When the population is normally distributed and the sample size is large, the t statistic can be approximated using the z score. This means that the t-distribution can be replaced with the standard normal distribution.

It is important to note that the other conditions mentioned in the options are not necessary for approximating the t statistic using the z score. These conditions may be relevant for other aspects of hypothesis testing, but not specifically for the approximation of the t statistic.