A group of high-school parents in Tucson, Arizona, inconjunction with faculty from the University of Arizona, claim thatyoung women in the Tucson high schools not only are called on lessfrequently, but receive less time to interact with the instructorthan do young men. They would like to see the school district hirea coordinator, spend money (and time) on faculty workshops, andoffer young women classes on assertiveness and academiccommunication.
To make things simple, assume that instructor interactions withyoung men average 95 seconds, with standard deviation 35 seconds.(Treat this as population information.)
The null hypothesis will be that the average interaction timefor young women will also be 95 seconds, as opposed to thealternate hypothesis that it is less, and will be tested at the2.5% level of significance.
- Give interpretations in context of Type I and Type II error inthis situation. (Your discussion should not focus on “Null” and“Alternate”.)
- What are the social, economic, and other consequences of(separately) Type I and Type II error?
- Find the rejection region for this test. That is, whatinteraction time bounds the lower 2.5% of the distribution?
- Assume the true mean interaction time for young women is 90seconds. Find the power of the test.
- Repeat part 4 for a true mean interaction time of 80seconds.
- What do the results in parts (4) and (5) mean in terms of yourprevious answers?
