Question

Two groups are tested in an experiment and the results for the measurements are: Group 1: 5, 7, 5, 3, 5, 3, 3, 9 Group 2: 8, 1, 4, 6, 6, 4, 1, 2 Test for the equality of the means at 5% significance. What is the 95% confidence interval for the difference in means?

Answer 1

Let denote the true mean for group 1 and group 2.

To test against

The test statistic can be written as

which under H₀ follows a t distribution with df.

where pooled variance

We reject H₀ at 5% level of significance if

Here

The value of the test statistic

and critical value

Since ,we fail to reject H₀ at 5% level of significance and we can conclude that the two means are not significantly different.

a 95% confidence interval for the difference in means