To study the effectiveness of a certain adult reading program, researchers will select a random sample of adults who are eligible for the program. The selected adults will be given a pretest before beginning the program and a posttest after completing the program. The difference in the number of correct answers on the pretest and the number of correct answers on the posttest will be recorded for each adult in the sample.

The matched pair t-interval for a population mean difference.

Step-by-step explanation:

The matched pair design (Used in the paired t-test or paired-samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.

A (1 - α)% confidence interval for matched pair design can be used to determine whether there is any difference between the two groups of data.

We use the paired t-interval if we have two measurements on the same item, person or thing. We should also use this interval if we have two items that are being measured with a unique condition.

For instance, an experimenter tests the effect of a medicine on a group of patients before and after giving the doses.  

In this case a study was conducted to determine the effectiveness of a certain adult reading program.

The selected adults will be given a pretest before beginning the program and a post-test after completing the program. Then the difference between the two scores would be computed for each adult.

This is an example of matched pair design.

To analyze this data, i.e. to determine whether the program is effective or not, compute the matched pair t-interval for a population mean difference.

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!