Question

Consider a hypothesis test of difference of means for two independent populations x1 and x2. Suppose that both sample sizes are greater than 30 and that you know σ1 but not σ2. Is it standard practice to use the normal distribution or a Student's t distribution?

A. Use the Student's t distribution because we do not know σ2.
B. Use the normal distribution because both sample sizes are greater than 30.
C. Use the Student's t distribution because both sample sizes are greater than 30.
D. Use the normal distribution because we do not know σ2.

Answer 1

To test the difference of means for two independent populations when the standard deviation of one population is known but not the other, it is standard practice to use the Student's t distribution.

Step-by-step explanation:

When performing a hypothesis test of difference of means for two independent populations, x1 and x2, and knowing the standard deviation of one population (σ1) but not the other (σ2), it is standard practice to use the Student's t distribution.

This is because the Student's t distribution is used when the population standard deviation is unknown and the distribution of the sample mean is approximately normal. Both sample sizes being greater than 30 allows for an approximation of the normal distribution to be used, even though the true v is the Student's t distribution.