Assume a research wants to test if a new drug is better at reducing the average

Question

Assume a research wants to test if a new drug is better at reducing the average pain score, and they have four groups : a placebo (P), a control (C), a standard drug group (S), and the new drug group (D).
(a) State the null hypothesis in mathematical symbols.

(b) State the alternative hypothesis.

(c) Interpret a Type I error in terms of the problem.

(d) Interpret a Type II error in terms of the problem.

(e) If we rejected the null hypothesis in this case, would we immediately be able to say that all group have signicantly dierent averages from each other?

Explanation / Answer

( a )

Null Hypothesis:

H0: µP = µC = µS = µD

( b )

Alternative Hypothesis:

H1: : µP µC µS µD

( c )

Type I Error: Reject the null hypothesis when the null hypothesis is true.

Here the type I error occur when we conclude that the new drug is better at reducing the average pain score but actually the new drug is not better at reducing the average pain score.

( d )

Type I Error: Accept the null hypothesis when the null hypothesis is false.

Here the type I error occur when we conclude that the new drug is not better at reducing the average pain score but actually the new drug is better at reducing the average pain score.

( e )

If we reject the null hypothesis null hypothesis then we can say that at least one of the mean differs. We cannot say that all groups have significantly different averages from each other.

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