The comparison distribution for a t test for independent means is a t distribution instead of a normal curve because
A)tables are not available for the normal curve.
B)the population variance is estimated.
C)Z distributions were not used at the time the t test for independent means was invented.
D)there are more degrees of freedom for two samples than for one.

Question

Quizplus · Accepted Answer

The population variance is not typically known in a t test for independent means, so it must be estimated from the sample variances. This introduces extra variability into the calculations, making the distribution of the test statistic more spread out and flatter than the normal curve. The t distribution adjusts for this by taking into account the sample size and the estimated variance, resulting in a distribution that closely approximates the normal curve but with slightly thicker tails.

The Comparison Distribution for a T Test for Independent Means