I need help answering the following three questions for each word problem below:

1. Is the t-test for this problem independent or dependent? Why?

2. Is the t-test directional or non-directional? Why?

3. What are the null and alternative hypotheses (mathematically stated)?

Word Problem 1:

A researcher wishes to learn if a certain drug affects the reaction time of pilots to air traffic

control instructions. She obtained a sample of pilots and randomly divided them into two groups.

She then had one pilot group take the drug and used the second group as a control. Pilots were

given headsets and given commands from an air traffic controller.

The researcher is interested in learning if the drug reduces the reaction time. Her hypothesis is:

The mean reaction time in group A will be less than the mean in group B.

A t-test can be used to test the probability that the two means do not differ. The alternative is that

the reaction times from the group treated with the drug will not be less than that from the control

group.

This is a one-tailed test because the researcher is interested in if the drug decreased reaction

time. She is not interested in if the drug changed reaction time.

Word Problem 2:

A researcher wishes to learn whether the GPA of incoming flight students may be a factor in the

number of flight hours the student completes in the first semester of college. The researcher has

collected the flight hours of a random sample of students in a group of high GPA students and

low GPA students.

The researcher is testing whether GPA may be a factor in differences in flight time accumulated

in the first semester at college.

Their hypothesis is: The mean flight time of students with a low GPA is different than those

incoming students with a high GPA.

A t-test can be used to test the probability that the two means do not differ. The alternative is that

the means differ; one of them is greater than the other.

This is a two-tailed test because the researcher is interested in if GPA changes flight time.