Suppose we have two independent, normally distributed, populations and we draw a random sample from each population. For population A, we drew a sample of 33 and found the mean to be 19 with a standard deviation of 7. For population B, we drew a sample of 32 with a mean of 21 and a standard deviation of 4. We want to determine if the treatments result in the same effect. Show all work.

What is the null and alternative hypothesis?

What is the rejection region at the 0.05 significance level? 0.01?

Using t, what is the value of the observed statistic?

What is the degree of freedom?

What is the p-value?

What conclusion can you draw at the 0.05 significance level? At the 0.01 significance level?