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Answer:
The power of the test is 0.67.
Step-by-step explanation:
The complete question is:
A researcher is evaluating the influence of a treatment using a sample selected from a normally distributed population with a mean of μ = 80 and a standard deviation σ = 20. The researcher expects a 12-point treatment effect and plans to use a two-tailed hypothesis test with α = 0.05. Compute the power of the test if the researcher uses a sample of n = 16 individuals .
Solution:
The information provided are:
The expected mean is:
The critical <em>z</em>-score at <em>α</em> = 0.05 for a two-tailed test is:
<em>z</em> = 1.96
*Use a <em>z-</em>table.
Compute the test statistic value as follows:
The power of statistical test is well-defined as the probability that we reject a false null hypothesis.
Power = Area to the right of the critical <em>z</em> under the assumption that H₀ is false.
Location of critical <em>z</em> (in H₀ is false distribution) =
This is negative because the critical z score is to the left of the mean of the H₀ in false distribution.
Area above z = -0 .44.
Compute the value of P (Z > -0.44) as follows:
Thus, the power of the test is 0.67.