Error probabilities You read that a statistical test at the α=0.01 level has probability 0.14 of

Name: Problem 24, Chapter 9: The Practice of Statistics for AP
Uploaded: 2020-04-12T19:28:55-08:00
Duration: 1 min 12 s
Channel: Andrew Shoemaker
Description: Error probabilities You read that a statistical test at the α=0.01 level has probability 0.14 of making a Type II error when a specific alternative is true. What is the power of the test against this alternative?

step 1 A statistical test at an alpha of 0 .01 level has a probability of 0 .14 of making a type 2 erro

Error probabilities You read that a statistical test at the...

Error probabilities You read that a statistical test at the $\alpha=0.01$ level has probability 0.14 of making a Type II error when a specific alternative is true. What is the power of the test against this alternative?

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Key Concepts

Significance Level

The significance level, often denoted by alpha (?), is the threshold used in hypothesis testing to determine when to reject the null hypothesis. It represents the probability of committing a Type I error, which is rejecting a true null hypothesis. This level is established prior to testing and helps control the rate of false positives.

Type II Error

A Type II error occurs in hypothesis testing when the test fails to reject a false null hypothesis, essentially missing a true effect or difference that actually exists. This concept is critical because it helps to understand the risk of false negatives in statistical tests.

Power of a Test

The power of a statistical test is the probability of correctly rejecting a false null hypothesis, or in other words, the test's ability to detect an effect when there is one. It is calculated as one minus the probability of a Type II error, and a higher power indicates a greater likelihood of detecting a true effect.

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