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

The correct distribution to use when testing the difference between the means of two populations with known variances and independent simple random samples is the normal distribution. Therefore, the correct answer is A. T distributions are only used when the population variances are unknown or when the sample sizes are small. Since the variances are known and the sample sizes are relatively large (n₁ = 38 and n₂ = 42), the normal distribution can be used to approximate the sampling distribution of the difference between the sample means.

Independent Simple Random Samples Are Taken to Test the Difference