Question

We have found that students who study by giving themselves quizzes recall a greater proportion of words than students who study by reading. Also, we see that there is an effect, but often the question of interest is not ‘‘Is there an effect?” but instead ‘‘How big is the effect?” To address this second question, use the information given below to find a 90% confidence interval for the difference in proportions p1 - p2, where p1 represents the proportion of items correctly recalled by all students who study using a self-quiz method and p2 represents the proportion of items correctly recalled by all students who study using a reading-only approach. Assume that the standard error for a bootstrap distribution of such differences is also about 0.07.

The proportion of items correctly recalled was 0.15 for the reading-study group and 0.42 for the self-quiz group. Round your answers to two decimal places.

The 90% confidence interval is

Answer 1

We need to construct the 90% confidence interval for the difference between population proportions p1​−p2​. We have been provided with the following information about the sample proportions:

Sample Proportion 1	0.15
Sample Size 1 (N1​) =	100
Sample Proportion 2	0.42
Sample Size 2 (N2​=)	100

The critical value for \alpha = 0.1α=0.1 is The corresponding confidence interval is computed as shown below:

Therefore, based on the data provided, the 90\%90% confidence interval for the difference between the population proportions p1​−p2​ is−0.37<p<−0.17, which indicates that we are 90\%90% confident that the true difference between population proportions is contained by the interval (-0.37, -0.17).

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