Final answer:
The statement 'To be able to use t in a test to compare two population means, the population variance must be known.' is False. In order to compare two population means using the t-test, the population variances do not need to be known.
Step-by-step explanation:
The statement 'To be able to use t in a test to compare two population means, the population variance must be known.' is False. In order to compare two population means using the t-test, the population variances do not need to be known. Instead, the t-test assumes that the population variances are equal.
For comparing two population means, the t-test is used when the population variances are unknown but assumed to be equal. This is known as the pooled t-test.
Example: Suppose we have two independent samples with sample sizes n1 and n2, sample means x1 and x2, and sample variances s1^2 and s2^2. If the null hypothesis is that the population means are equal, we can perform a pooled t-test by calculating the pooled standard deviation:
s_pooled = sqrt(((n1-1)s1^2+(n2-1)s2^2)/(n1+n2-2))
Then, we can calculate the t-statistic by:
t = (x1 - x2) / (s_pooled * sqrt(1/n1 + 1/n2))
Finally, we can compare the calculated t-value to the critical t-value at the desired significance level to make a decision.