Answer to Question #44175 in Statistics and Probability for Julie

Question

What can you say about two groups with information as follows?

Group A: o=24, s=3
Group B: o =27, s=5

Answer 1

Sample standard deviation of Group B is almost twice as much as sample standard deviation of Group A. It is obvious that population standard deviations are different in these groups. Next, we test whether means are different in groups. We can choose a two-sample hypothesis test. There is no sufficient information to answer this question. The first step is to discuss whether these groups are independent or related (measurements taken from the same individual). The second step is to discuss whether observations in groups are normally distributed or sample sizes of groups are large. The third step is to discuss whether we do not know population standard deviations at all or we know them (for example, from experience). To conclude, we need sample sizes of groups as well. There can be five different tests in this problem, but we exclude the case of equal standard deviations. There remain four cases.