A school has been using an innovative but largely untested f

A school has been using an innovative, but largely untested, fitness curriculum for several years. There is a growing concern among some parents that the curriculum is actually compromising, not facilitating, the student fitness levels. As evidence, the parents point to the 9th graders’ performance on the President’s fitness test that is administered each year at this school. When recently tested, the 121 9th graders in this school obtained a mean of 75. (For this test the national statistics are, m= 78 and o= 12.)

A school board meeting is coming up with this issue on the agenda. The superintendent, who knows that you are among the statistically enlightened, hires you to answer the question, “Is the performance of these 9th graders significantly lower than that of the population of 9th graders?”

a. Why does this scenario call for the one-sample z test?

b. What is the appropriate null hypothesis?

c. Specify - and explicitly justify - your choice of alternative hypothesis.

d. Calculate the test statistic, z.

e. What is the probability associated with this test statistic?

f. What is your statistical decision (a= .01)? How did you arrive at this decision?

g. What is your substantive conclusion? (Make sure that it does not sound like a statistical conclusion.)

h. In plain english, what would you tell the local school board about the tenability of the parents’ concern?

Solution