Chapter 20, Problem 2E

(a)

To determine

To write the null and alternative hypotheses you would use to test each of the situations given.

Answer to Problem 2E

  $\begin{array}{l}{H}_0:p=0.4\\ H_a:p\ne 0.4\end{array}$

Explanation of Solution

It is given in the question that only about $40\%$ of high school graduates went on to college. Has the percentage changed. Thus, the null hypothesis states that the percentage of high school graduates went on to collegeis $40\%$ . And the alternative hypothesis states that the percentage of high school graduates went on to college is not equal to $40\%$ . So, we have,

  $\begin{array}{l}{H}_0:p=0.4\\ H_a:p\ne 0.4\end{array}$

(b)

To determine

To write the null and alternative hypotheses you would use to test each of the situations given.

Answer to Problem 2E

  $\begin{array}{l}{H}_0:p=0.2\\ H_a:p<0.2\end{array}$

Explanation of Solution

It is given in the question that $20\%$ of cars of a certain model have needed costly transmission work after being driven. Thus, in this situation we can say that the null hypothesis states that the percentage of cars of a certain model have needed costly transmission work after being driven is equal to $20\%$ . And the alternative hypothesis states that the percentage of cars of a certain model have needed costly transmission work after being driven is less than $20\%$ . So, we have,

  $\begin{array}{l}{H}_0:p=0.2\\ H_a:p<0.2\end{array}$

(c)

To determine

To write the null and alternative hypotheses you would use to test each of the situations given.

Answer to Problem 2E

  $\begin{array}{l}{H}_0:p=0.6\\ H_a:p<0.6\end{array}$

Explanation of Solution

It is given in the question thatwe field-test a new-flavour soft drink, planning to market it only if we are sure that over $60\%$ of the people like the flavour. Thus, in this situation we can say that the null hypothesis states that percentage of the people like the flavour is equal to $60\%$ . And the alternative hypothesis states that percentage of the people like the flavour is less than $60\%$ . So, we have,

  $\begin{array}{l}{H}_0:p=0.6\\ H_a:p<0.6\end{array}$