AS/A2 Stats 1 Stats 2

S3 Topic 3: Estimation, confidence intervals and tests
The difference between means of two distributions (with known variance)
A null and alternative hypothesis for the difference between two population mean will be suggested, where m1 and m2 refer to the population means, and a level of test. You will be given the two population standard deviations, s1 and s2, too and the mean and size of samples from each population. To decide if the hypothesis test should have a non-significant or significant result based on those sample means, you will have to work out the test statistic, using:
and compare it with the critical value. The examples given will involve two-tailed tests.

Summary The above examples assume that the variances of the parent populations are known. In cases where these values are not known (a more realistic scenario), then the samples must be used to find unbiased estimates of the population variances. Provided the sample sizes are large, this will provide a reasonable accurate method. The values in the above formula of s12 and s22 should be replaced by these unbiased estimates. This page uses HotEqn.