Chapter 10, Problem AP3.28CPT

Y1

To determine

To find from the following options that which of the following represents the appropriate null and alternative hypotheses.

Answer to Problem AP3.28CPT

Option (d) is the correct option.

Explanation of Solution

It is given that we are interested in whether students at this high school are getting too little sleep or not.

Now, we are to construct the null and alternative thus, the null is equal to the hypothesized value. That is, if we look in the option then the sample mean is $7.9$ , this is not the hypothesized value, the hypothesized value is $9$ . In the same way, the alternative hypothesis determines whether or not the test is a left tail or right tail i.e. one tailed test or both left and right i.e. two tail test.

Since the researcher is specifically looking for too little sleep for the students then, we are interested in whether or not the students are getting less sleep that is, left tail test. If we are interested in the students getting too much sleep, it'd be a right tail test. So, in conclusion we have that,

  $\begin{array}{l}{H}_0:\mu =9\\ H_a:\mu <9\end{array}$

And that is the option (d). Thus, option (d) is the correct option.