A researcher is studying the weight changes that women go through over the course of pregnancy, childbirth and subsequent months. She recruits 194 women to take part in the study. Each woman is accurately weighed at the beginning of her fourth month of pregnancy. Some of the women (who we will call "the rememberers", n=188) are able to report what they weighed before they became pregnant. Others (who we will call "the forgetters", n=6) do not know what they weighed prior to pregnancy. The data are given below (weights in kg, n=group size)
Sample n Mean StDev
1 188 67 12
2 6 83 18
(a) Test the hypothesis that the mean weight for the forgetters is the same as that for the rememberers. Check whether you should assume equal variances. Use the conservative rule for degrees of freedom. State your null and alternative hypotheses formally, state your test statistic, and quote the critical value from the t tables. State your final conclusion in plain language.
(b) This time assume the two groups have equal variances. Construct a 99% confidence interval for the difference in mean weight between the two groups. Is zero (0) inside the confidence interval? Comment on what you can conclude from this.