Pharmaceutical scientists tested the effectiveness of a new drug designed to cure malaria. They randomly
assigned 400 infected lab rats to receive either the new drug or an existing drug and recorded how many
rats were cured at the end of the study. Here are their results:
Cured
Not
Total
New drug
176
24
200
Existing drug
168
32
200
They want to use these results to construct a 99% confidence interval to estimate the difference in the
proportion of these rats that would be cured under each drug (new - existing). Assume that all of the
conditions for inference have been met.
Which of the following is a correct 99% confidence interval based on their data?
8 +0.068
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joaobezerra 2 years ago
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Using the z-distribution, as we are working with a proportion, it is found that the 99% confidence interval is (-0.049, 0.129).

### What is the mean and the standard error for the distribution of differences?

For each sample, we have that:

Hence, for the distribution of differences, the mean and the standard error are given as follows:

### What is the confidence interval?

It is given by:

99% confidence level, hence, z is the value of Z that has a p-value of , so the critical value is z = 2.575.

Then:

The 99% confidence interval is (-0.049, 0.129).