10.4 – Inference as Decision

Additional Notes

• If you state parameter, you do not need to state hypotheses in words

• If not a random sample, you may not be able to generalize your results to the larger population.

• You do need to verify assumption that pop >10 x sample in order to use formula for standard deviation.

Decisions

• Choosing a fixed significance level, α, beforehand points to the outcome of the test as a decision. – If results are significant at level α, we reject Ho in

favor of Ha. Otherwise we fail to reject Ho.

Types of ErrorHo True Ha True

Reject Ho Type I error Correct Decision

Accept Ho Correct Decision Type II Error

Probability of Type I Error

• Type I error occurs when you reject Ho, but Ho is true.– The probability of this happening is equal to the

significance level of the test, α.

Probability of Type II Error

• Type II error occurs when we accept Ho even though Ho is not true. The probability of this happening is the probability that the test statistic falls between your critical values.

Power

• The probability that a fixed level significance test will reject Ho when a particular alternative value (Ha) of the parameter is true.

• The power of a test against any alternative is 1 minus the probability of a Type II error (β) for that alternative.

• Power = 1- β

Increasing the Power

• Increase α• Consider a particular alternative that is farther

away from μo. • Increase sample size• Decrease σ.