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# Board Review Week 2 Test - page 19 / 81

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When a researcher uses hypothesis testing, the researcher can never be certain that the conclusion he/she draws is correct. The decisions a researcher makes versus the truth can be portrayed by the following table.

Correct Decision

Type II Error (Probability )

RESEARCHER ACCEPTS Ha

Type II Error (Probability )

Correct Decision

RESEARCHER ACCEPTS Ho

Ha True

Ho True

TRUTH

If H0 is true, but by chance the data suggested strong enough evidence against H0 to reject H0, then a type I Error has been committed. The probability of a Type I Error is the -level of the test. Therefore, if = 0.01, then only 1% of the time will data be strong enough to reject H0 when H0 is true, resulting in a Type I Error.

If Ha is true, but the evidence against H0 was not strong enough to reject H0, then a Type II Error has been committed. The power of a test is defined as the probability of rejecting H0 when Ha is in fact true (the ability of the test to correctly identify a significant difference). The power of a test is directly related to the probability of committing a Type II Error. The probability of a Type II Error is and the power of a test is given by (1 - ). One of the most common reasons for a Type II Error is due to sample size being too small. In general, the larger the sample size, the greater the power of the test.

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