Question 1:
A food research laboratory conducts a series of taste tests to compare two sauce recipes, A and B. Customers are presented with the sauces in random order. Of the 125 customers who tried sauce A first, 74 expressed a preference for sauce A. Of the 132 customers who tried sauce B first, 52 expressed a preference for sauce A.
(a) Looking at the data in total, calculate a 95% confidence interval for the overall proportion of customers who prefer sauce A. Does this confidence interval contain 0.5? What conclusion could you draw from this.
(b) Test the hypothesis that the proportion of customers who prefer sauce A is the same for those who try sauce A first, as for those who try sauce B first. State your null and alternative hypotheses clearly, your test statistic, p-value, and conclusion.
Question 2:
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.