Question

Bisphenol A in Your Soup Cans Bisphenol A (BPA) is in the lining of most canned goods, and recent studies have shown a positive association between BPA exposure and behavior and health problems. How much does canned soup consumption increase urinary BPA concentration? That was the question addressed in a recent study \(^{34}\) in which consumption of canned soup over five days was associated with a more than \(1000 \%\) increase in urinary BPA. In the study, 75 participants ate either canned soup or fresh soup for lunch for five days. On the fifth day, urinary BPA levels were measured. After a two-day break, the participants switched groups and repeated the process. The difference in BPA levels between the two treatments was measured for each participant. The study reports that a \(95 \%\) confidence interval for the difference in means (canned minus fresh) is 19.6 to \(25.5 \mu \mathrm{g} / \mathrm{L}\). (a) Is this a randomized comparative experiment or a matched pairs experiment? Why might this type of experiment have been used? (b) What parameter are we estimating? (c) Interpret the confidence interval in terms of BPA concentrations. (d) If the study had included 500 participants instead of \(75,\) would you expect the confidence interval to be wider or narrower?

Short answer

a) This is a matched pairs experiment, which likely was used to control confounding variables. b) The parameter being estimated is the difference in population means of BPA concentrations after consuming canned versus fresh soup. c) A \(95 \%\) confidence interval for the difference in means, \(19.6 \mu \mathrm{g} /\mathrm{L} \) to \(25.5 \mu \mathrm{g} / \mathrm{L}\), suggests a significant increase in urinary BPA concentration after consuming canned soup. d) With 500 participants instead of 75, the confidence interval would likely be narrower.

Step-by-step solution

Identifying the type of experiment and its use

This is a matched pairs experiment. Each participant is subjected to both treatments, and the responses are measured. This type of experiment might have been used to control potential confounding variables, such as differences in individual's metabolism, in order to isolate the effect of the treatments on BPA levels. The matching helps to reduce the variability caused by these confounding variables.

Determining the Parameter Being Estimated

The parameter being estimated here is the difference in population means of urinary BPA concentrations after consuming canned soup and fresh soup.

Interpreting the Confidence Interval

The \(95 \%\) confidence interval for the difference in means, \(19.6 \mu \mathrm{g} /\mathrm{L} \) to \(25.5 \mu \mathrm{g} / \mathrm{L}\), implies that we are \(95 \%\) confident that the true mean BPA concentration difference (canned minus fresh) falls within this range. This suggests that consuming canned soup significantly increases urinary BPA concentration compared to fresh soup.

Effect of Sample Size on the Width of Confidence Intervals

If the study had included 500 participants instead of 75, we would expect the confidence interval to be narrower. This is because the standard error, which is the standard deviation divided by the square root of the sample size, decreases as the sample size increases. A smaller standard error implies a narrower confidence interval.