Question

A double-blind, randomly allocated medical experiment is comparing two possible treatments for an immune-system disorder. Patients are randomly assigned to two treatment groups.

	response	no response
treatment A	45	120
treatment B	95	70

[a] Calculate the percentage of patients who showed improvement in each treatment group. Round to the nearest tenth of a percent.

Pˆ A =

Pˆ B =

[b] Calculate a 95% confidence interval (2PropZInt) for the difference ( Pa-Pb) between the improvement rates.

(i) What is the center of the confidence interval? What does it measure?

(ii) Does one treatment seem to have about a 20-percentage point better effectiveness or not? Why?

Answer 1

We are given

	response	no response	Total
treatment A	45	120	165
treatment B	95	70	165

[a]

[b]   We know that

Hence, the 95% confidence interval is given by

i) The confidence interval is centered at

This confidence interval shows that we are 95% confident the difference between these population proportion will lie between (-0.40, -0.20).

ii) As we can see the 95% confidence interval of is (-0.40 , -0.20). This means that treatment B have minimum 20 percentage point better effectiveness and maximum 40 percentage point better effectiveness than treatment A.