A researcher wishes to determine whether listening to music affects students' performance on memory test. He randomly selects 50 students and has each student perform a memory test once while listening to music and once without listening to music. He obtains the mean and standard deviation of the 50 "with music" scores and obtains the mean and standard deviation of the 50 "without music scores".

1. Indicate the correct test procedure and reasoning.

O Two-sample t-test, since the researcher has two samples.

O Paired t-test, since there is a "with music" and "without music" score for each person.

O z-test for each sample, since the researcher has the sample standard deviation.

O Not enough information given to determine correct type of test.

O Pooled t-test, since the standard deviation is likely to be the same in both populations.

The correct option is option (2).

Step-by-step explanation:

The paired t-test (also known as the dependent 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.

We use the paired t-test if we have two measurements on the same item, person or thing. We should also use this test 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 the data is collected for the memory test once with music and again without music.

This implies that two set of observations are recorded for the same group of individuals.

This is an example of paired data.

So, a paired t-test will be used to test whether listening to music affects students' performance on memory test.

Thus, the correct option is option (2).