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Posts: 227
3 weeks ago
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.

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

Stats: Modeling the World


Edition: 4th
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Answer verified by a subject expert
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Posts: 274
3 weeks ago
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Conditions:
* Randomization Condition: The treatments were randomly assigned to subjects.
* 10% Condition: Not necessary for an experiment.
* Independent samples condition: The two groups are independent of each other because the treatments were assigned at random.
* Success/Failure Condition: For Brand C, 22 were drowsy and 58 were not. For Brand I, 14 were
drowsy and 66 were not. The observed number of both successes and failures in both groups is larger than 10.

Because the conditions are satisfied, we can model the sampling distribution of the difference in
proportions with a Normal model.

We know: nI = 80,  I = 0.175,  nC = 80,  C = 0.275
We estimate SD(C - I) as
SE(C - I) = = = 0.066
ME = z* × SE(C - I) = 1.96(0.066) = 0.128
The observed difference in sample proportions = C - I = 0.275 - 0.175 = 0.10, so the 95% confidence interval is 0.10 ± 0.128, or (-0.028, 0.228)

We are 95% confident that the difference between the proportions of patient that would have reported drowsiness had they all had Brand C and the proportion that would have reported drowsiness had they all had Brand I is between -2.8% and 22.8%.
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wrote...
3 weeks ago
TY
wrote...
3 weeks ago
Welcome Slight Smile
wrote...
3 weeks ago
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.

Would you make the same conclusion as question 2 if you conducted a hypothesis test? Explain.
wrote...
3 weeks ago
A hypothesis test at a 0.05 level should reach the same conclusion if a two-sided test is used. If the
alternate hypothesis were "less drowsy", the significance level would need to be changed, or a
different conclusion could occur.
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