Question

Questions on a statistics exam are considered good questions provided the questions discriminate between students who have studied for the exam and those who have not studied. Suppose that on a particular statistics exam the students were separated into two groups, the group that studied and the other group that had not studied. Data was collected and a 95% confidence interval for the difference in the proportion of those passing the exam from the group that studied and the proportion of those passing the exam from the group that had not studied. The confidence interval turned out to be (-0.005,0.125). Note that sample 1 is from the group that studied and sample 2 is from the group that did not study. Select the best answer.

Choose one answer.

A. The data fails to show with 95% confidence that these questions discriminated between those who studied and those who did not study.
B. We are 95% confident that those who studied had a higher passing rate than those who did not study.
C. We are 95% confident that those who studied had a lower passing rate than those who did not study.
D. None of the these are correct.

Answer 1

D. None of the these are correct.

Explanation:

Hello!

The students of a statistic class were separated in two groups for an exam (those who studied - groups 1- and those who didn't study- group 2-) after the exam the proportions of students that passed in both groups were calculated and a 95% CI for the difference of proportions was obtained: (-0.005,0.125)

If the parameter estimated was p₁ - p₂

If the questions discriminated between the students that studied and the students that did not study, then the proportions of both groups should be different, then the hypotheses are:

H₀: p₁ - p₂=0

H₁: p₁ - p₂≠0

To use a CI to decide over a hypotheses pair several conditions should be met:

1) The hypothesis should be two.tailed.

2) Both the hypothesis and the interval should study the same parameter.

3) The confidence level and significance level should be complementary, meaning if the interval was constructed with 1 - α: 0.95 then the test should be made with a level of α: 0.05.

If the conditions are met, then you can decide using the following rule:

If the CI contains the value stated in the null hypothesis, the decision is to not reject the null hypothesis.

If the CI doesn't contain the value stated in the null hypothesis, then the decision is to reject the null hypothesis.

Since "zero" is contained by the given interval, the decision is to not reject the null hypothesis. The at 5% confidence level you can conclude that the questions didn't discriminate between the students that studied and the students that didn't study.

I hope it helps!