Assume you are running a power analysis to determine how many observations you w

Question

Assume you are running a power analysis to determine how many observations you would need to address the following research question.

The scenario: I want to collect SAT math test scores from a random subset of students in the B SCHOOL (this is my sample) and I want to test to see if they are significantly higher than mean for the general X student population. This should tell you the type of test to select in JMP for your power analysis.

Hypothesis: The sample B mean (619) is significantly higher than the X population mean (595)

Standard deviation of the X population is 36

I'd like to maintain a power of 0.8 for this test (= less than a 20% chance of making a Type II error)

I'd like to maintain a significance threshold of 0.05 (= less than a 5% chance of making a Type 1 error)

How many students do I need to sample to determine if this difference between the X population and B subsample is significant?

Explanation / Answer

Using Minitab

Power and Sample Size

1-Sample Z Test

Testing mean = null (versus > null)
Calculating power for mean = null + difference
= 0.05 Assumed standard deviation = 36

            Sample Target
Difference    Size   Power Actual Power
        24   14     0.8      0.802222

sample size required = 14

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