Chapter 21, Problem 2E

(a)

To determine

To find out is the alternative hypothesis one-sided or two-sided and what are the hypotheses.

Answer to Problem 2E

It is a two-sided event.

Explanation of Solution

It is given in the question that a college dining conducts a survey to see if the students prefer plastic or metal cutlery. Thus, let p be the proportion of students who prefer plastic then, we have,

  $\begin{array}{l}{H}_0:p=0.5\\ H_1:p\ne 0.5\end{array}$

Thus, it is a two-sided event.

(b)

To determine

To find out is the alternative hypothesis one-sided or two-sided and what are the hypotheses.

Answer to Problem 2E

It is two-sided.

Explanation of Solution

It is given in the question that in recent years, $10\%$ of college juniors have applied for study abroad. The dean’s office conducts a survey to see if that’s changed this year. Thus, let p be the proportion of juniors applying for study abroad then, we have,

  $\begin{array}{l}{H}_0:p=0.1\\ H_1:p\ne 0.1\end{array}$

As it is considering only two-side in the alternative hypothesis so, it is two-sided.

(c)

To determine

To find out is the alternative hypothesis one-sided or two-sided and what are the hypotheses.

Answer to Problem 2E

It is one-sided.

Explanation of Solution

It is given in the question that a pharmaceutical company conduct a clinical trial to see if more patients who take a new drug experience headache relief than the $22\%$ who claimed relief after taking the placebo. Thus, let p be the proportion of people who experience relief then, we have,

  $\begin{array}{l}{H}_0:p=0.22\\ H_1:p>0.22\end{array}$

Thus, it is considering only one-side in the alternative hypothesis so, it is one-sided.

(d)

To determine

To find out is the alternative hypothesis one-sided or two-sided and what are the hypotheses.

Answer to Problem 2E

It is one-sided.

Explanation of Solution

It is given in the question that at a small computer peripherals company only $60\%$ of the hard drives produced passed all their performance test first time. Management recently invested a lot of resources into the production system and now conducts a test to see if it helped. Thus, let p be the proportion of hard drives that pass the test the first time then, we have,

  $\begin{array}{l}{H}_0:p=0.6\\ H_1:p>0.6\end{array}$

Thus, as it is considering only one-side in the alternative hypothesis so, it is one-sided.