Question

Suppose that we want to test the null hypothesis that the mean of population 1 is equal to the mean of population 2. We select a random sample from population 1 and a random sample from population 2, and these two samples are independent. Circle the FALSE statement.

A. We need to perform a two-sided test.

B. If we know the variance of each population, even if they are different, we can use the Z test. That is, the test statistic follows a normal distribution.

C. If we do not know the variance of each population, but we know the two populations share the same variance, then we can use the Z test. That is, the test statistic follows a normal distribution.

D. If we do not know the variance of each population, and we cannot assume the two populations share the same variance, then we can use the t test. That is, the test statistic follows a t distribution.

Answer 1

option A is correct because we have two samples and we want to test whether the two means are equal or not. So, it is a two tailed hypothesis

option B is correct because when we know the population variance, then we always use the z test and assume that the test statistic follows a normal distribution

option C is incorrect because when we dont know the population variance, then we cant use the z statistic to test the hypothesis. It is better to use t test statistic in this case when variances are unknown and equal.

option D is correct because we always use t test statistic when the variances are unknown and they are unequal.

therefore, answer is option C