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. Critical Student Mathematics Writing Reading 1 523 537 530 2 597 587 586 3 466 464 444 4 560 566 554 439 478 427 6 427 458 423 (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.

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(a) Using a 0.05 level of significance, do students perform differently on the three areas of the SAT?
A hypothesis test will be conducted to determine if students perform differently on the three areas of the SAT.
The null hypothesis, Ho, is a statement that is assumed to be true. The alternative hypothesis, Ha, 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.
Ho: HReading
= HMathematics
HWriting
Hai HReading + HMathematics
HWriting
Ho: At least two of the population means are equal.
: At least two of the population means are different.
Ho: HReading
+ HMathematics * HWriting
Ha: HReading = HMathematics
HWriting
%3D
Ho: Not all the population means are equal.
Ha: HReading = HMathematics
HWriting
Ho: HReading
HMathematics
HWriting
%3D
H: Not all the population means are equal.
Submit
Skip (you cannot come back),
Transcribed Image Text:(a) Using a 0.05 level of significance, do students perform differently on the three areas of the SAT? A hypothesis test will be conducted to determine if students perform differently on the three areas of the SAT. The null hypothesis, Ho, is a statement that is assumed to be true. The alternative hypothesis, Ha, 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. Ho: HReading = HMathematics HWriting Hai HReading + HMathematics HWriting Ho: At least two of the population means are equal. : At least two of the population means are different. Ho: HReading + HMathematics * HWriting Ha: HReading = HMathematics HWriting %3D Ho: Not all the population means are equal. Ha: HReading = HMathematics HWriting Ho: HReading HMathematics HWriting %3D H: Not all the population means are equal. Submit Skip (you cannot come back),
Tutorial Exercise
You may need to use the appropriate technology to answer this question.
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.
Critical
Student
Mathematics
Writing
Reading
1
523
537
530
2
597
587
586
3
466
464
444
4
560
566
554
439
478
427
6.
427
458
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.
Transcribed Image Text:Tutorial Exercise You may need to use the appropriate technology to answer this question. 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. Critical Student Mathematics Writing Reading 1 523 537 530 2 597 587 586 3 466 464 444 4 560 566 554 439 478 427 6. 427 458 423 (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.
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