Question

a. List three factors that will increase the power of a test.

b. What is the relationship between b, the probability of committing a Type II error, and the power of a test?

Short answer

a. Three factors:

• Increase the value of $\alpha$
• Sample size increase
• Distance between increase ${\mu }_{\alpha }$(that is,actual value) as well as the null hypothesis value.

b. Power of the test = $1-\beta$, where $\beta$ is the probability of committing type II error.

Step-by-step solution

(a) Three factors of increase the power test

The power of a test is the probability that testing will result in the null hypothesis being rejected for a given average value in the alternative hypothesis, and it is equivalent

to $1-\beta$.

Increasing the $\alpha$, decreasing the $\beta$, as well as increasing the sample size n are three parameters that will boost the power of a test.

1. Increase the value of $\alpha$
2. Sample size increase
3. Distance between increase ${\mu }_{\alpha }$(that is,actual value) as well as the null hypothesis value.

Step 2:(b) Relationship between b and the probability of committing a type II

Power of the test =$1-\beta$, where$\beta$is the probability of committing type II error.The probability of making a type II error is one minus the test's power, commonly known as beta. With a larger sample size, the power of the test can be enhanced, lowering the chance of making a type II mistake.

The link between $\beta$ and test power is $1-\beta$