Chapter 21, Problem 1E

(a)

To determine

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

Answer to Problem 1E

It is a two-sided event.

Explanation of Solution

It is given in the question that a business student conducts a taste test to see whether students prefer Diet Coke or Diet Pepsi. Thus, let p be the percentage of students who prefer Diet Pepsi 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 1E

It is one-sided.

Explanation of Solution

It is given in the question that PepsiCo recently reformulated Diet Pepsi in an attempt to appeal to teenagers. They run a taste test to see if the new formula appeals to more teenagers than the standard formula. Thus, let p be the proportion of teenagers who prefer the new formulation then, we have,

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

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

(c)

To determine

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

Answer to Problem 1E

It is one-sided.

Explanation of Solution

It is given in the question that a budget override in a small town requires a two-third majority to pass. A local newspaper conducts a poll to see if there is evidence it will pass. Thus, let p be the proportion of people who intend to vote for the override then, we have,

  $\begin{array}{l}{H}_0:p=\frac{2}{3}\\ H_1:p>\frac{2}{3}\end{array}$

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 1E

It is two-sided.

Explanation of Solution

It is given in the question that one financial theory states that the stock market will grow up or down with equal probability. A student collects data over several years to test the theory. Thus, let p be the proportion of days that the market goes up then, we have,

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

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