Chapter 9.3, Problem 66E

To determine

To check: Whether the conditions required to perform the hypothesis test for population mean are satisfied or not.

Answer to Problem 66E

Yes, the conditions are fulfilled.

Explanation of Solution

Given:

  $\begin{array}{l}\text{Hypothesized population mean}\left({\mu }_0\right)=19.2\\ \text{Sample size}\left(n\right)=75\\ \text{Level of significance}\left(\alpha \right)=0.10\end{array}$

The null and alternative hypotheses are:

  $\begin{array}{l}{H}_0:\mu =19.2\\ H_a:\mu \ne 19.2\end{array}$

Conditions for performing a hypothesis test about $\mu$ are:

• The samples taken from the population must be simple random samples.
• The sample size should be large that is, $n>30$ or the population should be distributed normally.

Requirement check:

• The sample of 75 bags of candy is assumed to be selected at random.
• The sample size is greater than 30.

Thus, both the required conditions are met.