Question

Suppose that someone claims that the mean income of two group of individuals is equal. In order to test that claim, a researcher collects two samples and finds that the one group earns $1,448 more on average than the other group. Is that sufficient evidence to reject the claim that the mean income in the two populations is equal? why?

Answer 1

No, this is not sufficient to reject the claim.

In order to make conclusions about the population means of two groups we need to make sure we have a good sample size, the sample is chosen randomly. Then we need to find the the sample variances of the groups as well as the variance tells us how much the individual values differ from the mean. Then based on all these we need to calculate the test statistic of the difference in means and compare it to an appropriate critical value at the given significance level. Only then we can Reject/fail to reject the hypothesis.