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
528
534
528
2
592
590
588
3
465
464
445
4
561
566
553
5
436
478
430
6
430
458
420
Using a 0.05 level of significance, do students perform
differently on the three areas of the SAT?
State the null and alternative hypotheses.
H0: 𝜇Reading = 𝜇Mathematics = 𝜇Writing
Ha: 𝜇Reading ≠ 𝜇Mathematics ≠ 𝜇Writing
H0: 𝜇Reading ≠ 𝜇Mathematics ≠ 𝜇Writing
Ha: 𝜇Reading = 𝜇Mathematics = 𝜇Writing
H0: 𝜇Reading = 𝜇Mathematics = 𝜇Writing
Ha: Not all the population means are equal.
H0: At least two of the population means are
equal.
Ha: At least two of the population means are
different.
H0: Not all the population means are
equal.
Ha: 𝜇Reading = 𝜇Mathematics = 𝜇Writing
Find the value of the test statistic. (Round your answer to two
decimal places.)
Find the p-value. (Round your answer to three
decimal places.)
p-value =
State your conclusion.
Reject H0. There is not sufficient
evidence to conclude that the mean scores for the three parts of
the SAT are not all equal.
Reject H0. There is sufficient evidence to
conclude that the mean scores for the three parts of the SAT are
not all equal.
Do not reject H0. There is not
sufficient evidence to conclude that the mean scores for the three
parts of the SAT are not all equal.
Do not reject H0. There is sufficient
evidence to conclude that the mean scores for the three parts of
the SAT are not all equal.
Which area of the test seems to give the students the most
trouble? Explain.
The mean test scores for the three sections are ? for
critical reading, ? for mathematics, and ? for writing.
Because the ? section has the lowest average score, this
section appears to give the students the most trouble.