Question

Restaurant power problems Refer to Exercises $86$ and $88$

a. Explain one disadvantage of using $\alpha =0.10$ instead of $\alpha =0.05$ when

performing the test.

b. Explain one disadvantage of taking a random sample of $50$ people instead of $30$ people.

Short answer

Part (a) There is the most likely to have a type I error.

Part (b) There is more time consuming and costly to collect the data.

Step-by-step solution

Part (a) Step 1: Given information

$$\begin{gathered} \alpha =0.05 \\ {H}_0:\mu =\$85,000 \\ \mu >\$85,000 \\ \mu =\$86,000 \end{gathered}$$

Part (a) Step 2: Explanation

Type I error: Reject the null hypothesis $H_0$, once the null hypothesis $H_0$is true.

$\alpha$Showing the probability of a type I error.

If you increase $\alpha =0.05to\alpha =0.10$ the likelihood of making a type I error increases, and you're more likely to make one, which is a negative.

Part (b) Step 1: Explanation

If the sample size is increased from $30$to $50$persons, collecting data for the $50$people will take longer and cost more money than collecting data for the $30$people (as there are about twice as many potatoes about which we need to gather information.).