Q. 77 - The Practice of Statistics for AP

Question

The power of tomatoes The researchers who carried out the experiment in Exercise $75$ suspect that the large P-value ($0.114$) is due to low power.

(a) Describe a Type I and a Type II error in this setting. Which type of error could you have made in Exercise $75$? Why?

(b) Explain two ways that the researchers could have increased the power of the test to detect .

Step-by-Step Solution

Answer

a. Type II error since we failed to reject $H_0$.

b. Increasing the significance level, decreasing the standard deviation $s_x$ or increasing the sample size.

Step 1: Given information

The researchers who carried out the experiment in Exercise $75$ suspect that the large P-value ($0.114$) is due to low power.

Step 2: Explanation (part a)

Type I error: experts conclude that Variety A has a higher mean yield when it actually doesn’t. 

Type II error: experts conclude that there is no mean difference in yields when, in fact,

Variety A has a higher mean yield. 

Type II error since we failed to reject $H_0$.

Step 3: Explanation (part b)

Increasing the significance level, decreasing the standard deviation $s_x$ or increasing the sample size.