Question

Potato power problems Refer to Exercises $85$ and $87$

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 $500$ potatoes instead of $250$ potatoes from the shipment.

Short answer

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

Part (b) More time-consuming and costly to collect the data.

Step-by-step solution

Part (a) Step 1: Given information

$$\begin{gathered} H_0:p=0.08 \\ {H}_a:p>0.08, \\ p=0.11, \\ n=500 \\ \alpha =0.05 \end{gathered}$$

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 $250$ to $500$ potatoes, data collection will be more time-consuming and costly for the $500$ potatoes than for the $250$ potatoes (as there are twice as many potatoes about which we need to collect data).