Question

Candy! A machine is supposed to fill bags with an average of 19.2 ounces of candy. The manager of the candy factory wants to be sure that the machine does not consistently underfill or overfill the bags. So the manager plans to conduct a significance test at the $\alpha =0.10$significance level of

$$\begin{gathered} H_0:\mu =19.2 \\ {H}_a:\mu notequalto19.2 \end{gathered}$$

where $\mu =$the true mean amount of candy (in ounces) that the machine put in all bags filled that day. The manager takes a random sample of 75 bags of candy produced that day and weighs each bag. Check if the conditions for performing the test are met.

Short answer

The required answer is:

Yes, the conditions are fulfilled.

Step-by-step solution

Given information

Hypothesized population mean $\left({\mu }_0\right)=19.2$

Sample size $\left(n\right)=75$

Level of significance $\left(\alpha \right)=0.10$

The null and alternative hypotheses are as follows:

$$\begin{gathered} H_0:\mu =19.2 \\ {H}_a:\mu notequalto19.2 \end{gathered}$$

The objective is to check whether the conditions required to perform the hypothesis test for the population mean are satisfied or not.

The following conditions must be met before conducting a hypothesis test on $\mu$:

Simple random samples must be drawn from the population.

The sample size should be large, $n>30$or the population should be normally distributed.

Requirement check:

The sample of $75$candy bags is assumed to be chosen at random.

The sample size exceeds $30$

Therefore, both the required conditions are met.