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Homework answers / question archive / You are considering testing a new drug that is supposed to facilitate learning in developmentally delayed children
You are considering testing a new drug that is supposed to facilitate learning in developmentally delayed children. Based on preliminary research, you have some idea about the size of the drug's effect. Because of your work schedule you can either do the test with 15 subjects or with 20. You would like to only run 15 subjects, but if running 20 will make power at least 20% higher, you will run 20 subjects.
Calculate power for the following conditions:
a.N = 15, a = .051 tail, Preal = 0.70. b.N = 20, a = .051 tail, Preal = 0.70. c.Based on your calculations, how many subjects will you test?
H0?:p?=0.5H1?:p?>0.5significancelevel,α=0.05?
a.
N = 15, a = .05 1 tail, P real = 0.70
standard deviation =??15(0.5)(1−0.5)??? = 0.1291
critical z value for 95% confidence = 1.6449
critical = 0.5 + 1.6449 * 0.1291= 0.7124
z assuming null hypothesis is false:
z =?????0.12910.7124−0.7??? = 0.0960
power = P(z > 0.0960) = 0.46176
b.
N = 20, a = .05 1 tail, Preal = 0.70.
standard deviation =???20(0.5)(1−0.5)????? = 0.1118
critical z value for 95% confidence = 1.6449
critical = 0.5 + 1.6449 * 0.1118= 0.6839
z assuming null hypothesis is false:
z =???????0.11180.6839−0.7????? = -0.1440
power = P(z > -0.1440) = 0.55725
c.
percentage increase in power = ?0.461760.55725−0.46176?? *100 = 20.6795 %
since the percentage increase in power is greater than 20%, we should go with 20 samples
