Question

A pharmaceutical company tests whether a drug lifts the headache relief rate from the 25% achieved by a placebo. The pharmacy runs a 1-Propoortion z-Test using the following hypotheses (try writing these out in words to help interpret in context):

a) What is a Type I Error in the context of this problem?

b) What is a Type II Error in the context of this problem?

Answer 1

Head-ache relief rate achieved by a placebo -> 25%

The drug tested by the pharma company is to improve the relief rate

H0: μ <= 25% (The pharma company drug doesn't lift the mean relief rate)

H1: μ > 25% (The pharma company drug lifts the mean relief rate)

a) Type-1 error: Rejection of a true null hypothesis

If H0 is true and is rejected, it is good in the context of the problem as the new drug improves the relief rate

b) Type-2 error is the non-rejection of a false null hypothesis

If H0 is false and is not rejected, it is bad in the context of the problem as the less effective placebo will be still used

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