5. Fourteen measurements of the bicarbonates (CO$_3$H) content X of the bottled water
sold by Smart Healthy Shoppers, a chain of drugstores, yielded the following
information (Note: X is in mg/L)
$\sum X = 4,956.0$
$\sum X^2 = 1,754,476.0$
(a) Find the 99% confidence limits of (i) the true mean and (ii) the true standard
deviation of the probability distribution of X. Assume that X is a normally
distributed random variable.
(b) Test the hypothesis that the mean value of the probability distribution of X is not
significantly different from 350.0mg/L. Let $\alpha = 0.05$.
(c) Test the hypothesis that the true standard deviation of the probability distribution
of X is not significantly different from 3.2 mg/L. Let $\alpha = 0.05$.
