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

Let me know if you need anything else, if not please don't
forget to like the answer :)

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