Chapter 9.3, Problem 65E

To determine

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

Answer to Problem 65E

Yes, the conditions are fulfilled.

Explanation of Solution

Given:

  $\begin{array}{l}\text{Hypothesized population mean}\left({\mu }_0\right)=115\\ \text{Sample size}\left(n\right)=45\\ \text{Level of significance}\left(\alpha \right)=0.05\end{array}$

The null and alternative hypotheses are:

  $\begin{array}{l}{H}_0:\mu =115\\ H_a:\mu >115\end{array}$

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 45 has been selected from simple random sampling technique.
• The sample size is greater than 30.

Thus, both the required conditions are met.