Name: 5. A researcher plans to conduct an experiment evaluating the effect of a

Question

Name: 5. A researcher plans to conduct an experiment evaluating the effect of a treatment. A sample of n = 9 participants is selected and each person receives the treatment before being tested on a standardized dexterity task. The treatment is expected to lower scores on the test by an average of 30 points. For the regular population, scores on the dexterity task form a normal distribution with = 240 and = 30. a. If the researcher uses a two-tailed test with = .05, what is the power of the hypothesis test? b. Again, assuming a two-tailed test with = .05, what is the power of the hypothesis test if the sample size is increased to n 25?

Explanation / Answer

a) H0 is true sampling distribution: µ = 240 M = / n = 30 / 9 = 10

H0 is false sampling distribution: µ = 240 + 30 = 270, M = 10

Critical z-score: = 0.05, two-tailed. Z = 1.96 (raw score = µ + z M = 240 + 1.96 * 10 = 259.6

Power = 30/10 = 3

Z = 3 – 1.96 = 1.04

b)

H0 is true sampling distribution: µ = 240 M = / n = 30 / 25 = 6

H0 is false sampling distribution: µ = 240 + 30 = 270, M = 6

Critical z-score: = 0.05, two-tailed. Z = 1.96 (raw score = µ + z M = 240 + 1.96 * 6 = 251.76

Power = 30/6 = 5

Z = 5 – 1.96 = 3.04

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