3. A researcher wishes to determine whether four commercially available standardized 3.

achievement tests differ in their popularity. He obtains a random sample of 60 school districts in his region of the country and asks each superintendent which standardized achievement test is used. (Assume that each district uses such a test, and only four tests exist.) The researcher has no basis for hypothesizing which test, if any, is preferred by school districts. The results are as follows:

Test A B C D Frequency of selection 18 6 12 24

(a) Give, in symbolic form, two equivalent statements of H0 for this situation.

(b) Can H1 be written in a single symbolic statement? (Explain.)

(c) Compute the expected frequencies under H0. (Do they sum to n?)

(d) Compute χ2 and test H0 at α 01.

(e) From this χ2 what is your general conclusion? That is, do the four achievement tests appear to differ in popularity?