Researchers conduct a study to test a potential side effect of a new allergy medication. A random sample of 160 subjects with allergies was selected for the study. The new "improved" Brand I medication was randomly assigned to 80 subjects, and the current Brand C medication was randomly assigned to the other 80 subjects. 14 of the 80 patients with Brand I reported drowsiness, and 22 of the 80 patients with Brand C reported drowsiness.

2) Compute a 95% confidence interval for the difference in proportions of subjects reporting drowsiness. Show all steps.

CI=(-0.0285,0.2285)

Step-by-step explanation

First, calculate the sample proportion for both brands.

p1?=8014?=0.175

p2?=8022?=0.275

Next, we find the standard error of proportion using the equation below.

Std.ErrorofProportion=np(1−p)??

For Brand I:

800.175(1−0.175)??=0.042482

For Brand C:

800.275(1−0.275)??=0.049922

Then, get the standard error for difference.

Std.ErrorofDifference=0.0424822+0.0499222?=0.065551

For the 95% confidence interval, we have:

CI=(p2?−p1?)±zα/2?(Std.ErrorofDifference)

CI=(0.275−0.175)±1.96(0.065551)

CI=0.1±0.12848

CI=(-0.0285,0.2285)

You could also use this equation and it would also yield the same results (there may be discrepancies due to the rounding of values in the solution above):

CI=(p1?−p2?)±zα/2?(np1?(1−p1?)?+np2?(1−p2?)??)

Note that p₁ and p₂ are interchangeable. If p₁ has the largest value, then p₂ must be subtracted from it.