You are interested in determining whether an experimental birth control pull has the side effects of...

You are interested in determining whether an experimental birth control pull has the side effects of changing blood pressure. You plan to randomly sample 18 women from the city in which you live. You give half of them a placebo for a month and then measure their diastolic blood pressure. Then you switch them to the birth control pill for a month and again measure their blood pressure. The other 9 women receive the same treatment except they are given the birth control pill first for a month, followed by the placebo for a month. The blood pressure readings are shown here. What is the power of your study to reject the null assuming that the alternative hypothesis is true. Assume alpha =.05 non directional alternative hypothesis. YOU DO NOT NEED ANY DATA IT ONLY LOOKS FOR POWER

What is the power to detect a false null hypothesis assuming Preal=.9. Put your work and answer below.

What is the probability of failing to reject the null if the null is false assuming Preal =.9. Put your work and answer below.

What is the power to detect a false null hypothesis assuming Preal=.7. Put your work and answer below.

What is the probability of making a type 2 error assuming Preal =.7. Put your work and answer below.

Solutions

Expert Solution

Power of a hypothesis test is the probability of correctly rejecting the null hypothesis when the null hypothesis is not true.

Type II error is the probability of failing to reject the null hypothesis if it is false. Hence Type II error is 1 minus power of the hypothesis test.

Power is 1 minus the probability of Type II error.

For Preal=0.9,

P(Type II error) = P(|z|>=0.9) = 2* P(z>=0.9) =2*(0.18406) = 0.36812

Power = 1- P(Type II error)= 0.63188

Hence the power to detect a false null hypothesis assuming Preal = 0.9 is 0.63188 and the probability of failing to reject the null if the null is false assuming Preal =0.9 is 0.36812

For Preal=0.7,

P(Type II error) = P(|z|>=0.7) = 2* P(z>=0.7)=2*(0.24196) = 0.48392

Power = 1- P(Type II error)= 0.51608

Hence the power to detect a false null hypothesis assuming Preal =0.7 is 0.51608 and the probability of making a type 2 error assuming Preal =0.7 is 0.48392

milcah answered 9 months ago

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