Chapter 22, Problem 16E

(a)

To determine

To find: the hypothesis test.

Answer to Problem 16E

  $\begin{array}{c}{\text{H}}_0:p_{prozac}-p_{placebo}=0\\ {\text{H}}_1:p_{prozac}-p_{placebo}>0\end{array}$

Explanation of Solution

  $H_0:\text{Between}\text{Placebo}\text{and}\text{Prozac,}\text{no}\text{difference}$

  ${\text{H}}_0:p_{prozac}-p_{placebo}=0$

  $H_1:\text{Prozac}\text{is}\text{more}\text{effective}\text{than}\text{Placebo}$

  ${\text{H}}_1:p_{prozac}-p_{placebo}>0$

(b)

To determine

To State: a conclusion based on confidence interval.

Explanation of Solution

It is failed to reject the null hypothesis because 0 is found within the confidence interval. There is no proof that Prozac is a successful medication.

(c)

To determine

To find: the test use of the alpha level.

Explanation of Solution

Since there have used a 95 percent confidence interval, one side is the alternative hypothesis. The alpha level test used is, thus,

  $\begin{array}{c}\alpha =\frac{100-95}{2}\%\\ =2.5\%\end{array}$

(d)

To determine

To find: the type of error makes if the inference is incorrect.

Answer to Problem 16E

Type II

Explanation of Solution

It is a Type II error because the null hypothesis failed to be dismissed when it was actually incorrect.

(e)

To determine

To find: the consequences of a mistake of this kind.

Explanation of Solution

It is a Type II error because the null hypothesis failed to be dismissed when it was actually incorrect. A potentially beneficial cure for anorexia will be ignored.