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Chapter 7: Q96E (page 439)

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

Expert verified

a. Three factors:

  • Increase the value of α
  • Sample size increase
  • Distance between increase μα(that is,actual value) as well as the null hypothesis value.

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

Step by step solution

01

(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-β.

Increasing the α, decreasing the β, as well as increasing the sample size n are three parameters that will boost the power of a test.

  1. Increase the value of α
  2. Sample size increase
  3. Distance between increase μα(that is,actual value) as well as the null hypothesis value.
02

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

Power of the test =1-β, whereβis 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 β and test power is 1-β

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