Is the t-test for this problem independent or dependent
Subject: Mathematics / Statistics
Question
1. Is the t-test for this problem independent or dependent? Why?
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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.
