The Scholastic Aptitude Test (SAT) contains three areas: critical reading, mathematics, and writing. Each area is scored on an 800-point scale. A sample of SAT scores for six students follows.

Student	Critical Reading	Mathematics	Writing
1	523	537	530
2	597	587	586
3	466	464	444
4	560	566	554
5	436	481	427
6	430	455	423

(a)Using a 0.05 level of significance, do students perform differently on the three areas of the SAT?

(b)Which area of the test seems to give the students the most trouble? Explain.

A hypothesis test will be conducted to determine if students perform differently on the three areas of the SAT. The null hypothesis, H₀, is a statement that is assumed to be true. The alternative hypothesis, H_a, is what the test is attempting to establish.

If students do not perform differently on the SAT, then the population means of the scores for each area will be the same. The alternative hypothesis for testing the equality of population means will always have the same form, that they are not all equal. Note that this does not necessarily mean that each population mean is different, just that they are not all the same value.

Therefore, we have the following hypotheses:

H₀: _Reading = _Mathematics = _Writing H_a: Not all the population means are equal.

Since the SAT scores for each area are given for each student, this is a randomized block design. In a randomized block design, there are k treatments and b blocks. The total sample size is n_T = kb.

There are three areas of the SAT tests, which can be viewed as the number of treatments. There are scores for each of six different students. The given scores are therefore blocked by students. This gives k = ____________ treatments and b = ____________ blocks. The total sample size is n_T=kb = ____________.