Making conclusions about the difference of proportions

A university offers a certain course that students can take in-person or in an online setting. Teachers of the course were curious if there was a difference in the passing rate between the two settings. Data from a recent semester showed that

80 %

of students passed the in-person setting, and

75 %

of students passed the online setting. They were willing to treat these as representative samples of all students who may take each setting of the course.

The teachers used those results to make a

95 %

confidence interval to estimate the difference between the proportion of students who pass in each setting of the course

(p_{in-person} - p_{online})

. The resulting interval was approximately

(- 0.04, 0.14)

. They want to use this interval to test

H_{0} : p_{in-person} = p_{online}

versus

H_{a} : p_{in-person} \neq p_{online}

. Assume that all conditions for inference have been met.

Based on the interval, what do we know about the corresponding P-value and conclusion at the $α = 0.05$ ‍ level of significance?

(Choice A)
The P-value is less than $α = 0.05$ ‍, and they should conclude that there is a difference between the proportions.
(Choice B)
The P-value is less than $α = 0.05$ ‍, and they cannot conclude that there is a difference between the proportions.
(Choice C)
The P-value is greater than $α = 0.05$ ‍, and they should conclude that there is a difference between the proportions.
(Choice D)
The P-value is greater than $α = 0.05$ ‍, and they cannot conclude that there is a difference between the proportions.

AP®︎/College Statistics

Course: AP®︎/College Statistics > Unit 10

Problem