Chapter 5.3, Problem 3Q

Mercury pollution is widely recognized as a serious ecological problem. Much of the mercury released into the environment originates as a byproduct of coal burning and other industrial processes. It does not become dangerous until it falls into large bodies of water, where microorganisms convert it to methylmercury $\left({\text{CH}}_{\text{3}}{\text{Hg}}^{\text{+}}\right)$, an organic form that is particularly toxic. Fish are the intermediaries: They ingest and absorb the methylmercury and are then eaten by humans. Men and women, however, may not metabolize ${\text{CH}}_{\text{3}}{\text{Hg}}^{\text{+}}$ at the same rate. In one study investigating that issue, six women were given a known amount of protein-bound methylmercury. Shown in the following table are the half-lives of the methylmercury in their systems $\left(121\right)$. For men, the average ${\text{CH}}_{\text{3}}{\text{Hg}}^{\text{+}}$ half-life is believed to be eighty days. Assume that for both genders, ${\text{CH}}_{\text{3}}{\text{Hg}}^{\text{+}}$ half-lives are normally distributed with a standard deviation $\left(\sigma \right)$ of eight days. Construct a 95% confidence interval for the true female ${\text{CH}}_{\text{3}}{\text{Hg}}^{\text{+}}$ half-life. Based on these data, is it believable that males and females metabolize methylmercury at the same rate? Explain.

Females	${\text{CH}}_{\text{3}}\text{Mg+}$ Half-Life
AE	52
EH	69
LJ	73
AN	88
KR	87
LU	56