Independent simple random samples are taken to test the difference between the means of two populations whose variances are known. The sample sizes are n1 = 38 and n2 = 42. The correct distribution to use is the
A) normal distribution
B) t distribution with 80 degrees of freedom
C) t distribution with 79 degrees of freedom
D) t distribution with 78 degrees of freedom

Question

Quizplus · Accepted Answer

When variances are known and sample sizes are larger than 30, the normal distribution can be used to test the difference between two means. In this case, both sample sizes are larger than 30, so the correct distribution to use is the normal distribution. Therefore, option A is the best choice. The t distribution would only be used if the variances were unknown or if the sample sizes were smaller than 30.

Independent Simple Random Samples Are Taken to Test the Difference