Determine the null and alternative hypotheses. State whether the test is two tailed, left-tailed, or right-tailed.

(a) The Medco pharmaceutical company has just developed a new antibiotic for children. Two percent of children taking competing antibiotics experience headaches as a side effect. A researcher for the Food and Drug Administration wishes to know if the percentage of children taking the new antibiotic who experience headaches as a side effect is more than \(2 \%\).

(b) The Blue Book price of a used three-year-old Chevy Corvette ZR1 is \(\$ 86,012\). Grant wonders if the mean price of a used three-year-old Chevy Corvette ZR1 in the Miami metropolitan area is different from \(\$ 86,012\).

(c) The standard deviation of the contents in a 64-ounce bottle of detergent using an old filling machine is 0.23 ounce. The manufacturer wants to know if a new filling machine has less variability.

Approach In each case, we must determine the parameter to be tested, the statement of no change or no difference (status quo), and the statement we are attempting to gather evidence for.