This note is directed to those interested in statistics or teaching AP
Statistics.
At Cate we use Basic Practice of Statistics, by David Moore.
I like the book... and all indications are that my students find it readable,
but there is one thing that bothers me.
When Moore gives examples of a one-tail test (hypothesis testing), he states
the null hypothesis in the form....
Ho: mean is equal to 12. (the number 12 is arbitrary here)
Then, he states the alternate hypothesis, Ha, in the form
Ha: mean is greater than 12.
There are numerous examples in the book where Moore does this. And... the
solutions manual does the same thing in providing suggestion responses to
problems.
Far-be-it for me to question the writings of someone of David Moore's status,
but it seems to me that the null hypothesis should be stated...
Ho: mean is equal to or less than 12.
Could someone unconfuse me here?
If x represents a real number, then there are three possibilities: (1) x=12,
(2) x>12, or (3) x<12. The null hypothesis (Ho) and the alternate hypothesis
(Ha) should cover all possible situations. The way Moore writes up his
examples (and, using the example above), if you reject the null hypothesis, you
certainly have to accept the possibility that the mean is less than 12 (which
is not equivalent to accepting Ha.)
I'd like to make sure my students understand hypothesis testing. So... I'd
appreciate any insight that anyone has on the above.
Thanks for your attention to this note. I enjoyed seeing many of you in
Minneapolis. Keep in touch.
Sanderson M. Smith