A standardized test consists of three parts: math, writing, and critical reading. Sample data showing the math and writing scores for a sample of 12 students who took the test follow. Student Math Writing 1 540 474 2 432 380 3 528 463 4 574 612 5 448 420 6 502 526 7 480 424 8 499 459 9 610 615 10 572 535 11 390 335 12 593 613 (a) Use a 0.05 level of significance and test for a difference between the population mean for the math scores and the population mean for the writing scores. (Use math score − writing score.) Formulate the hypotheses. H0: μd = 0 ; Ha: μd ≠ 0 H0: μd ≤ 0 ; Ha: μd = 0 H0: μd > 0 ; Ha: μd ≤ 0 H0: μd ≠ 0 ; Ha: μd = 0 H0: μd ≤ 0 Ha: μd > 0 Calculate the test statistic. (Round your answer to three decimal places.) = Calculate the p-value. (Round your answer to four decimal places.) p-value = What is your conclusion? (A) Do not reject H0. We cannot conclude that there is a significant difference between the population mean scores for the math test and the writing test. (B) Reject H0. We cannot conclude that there is a significant difference between the population mean scores for the math test and the writing test. (C) Do not reject H0. We can conclude that there is a significant difference between the population mean scores for the math test and the writing test. (D) Reject H0. We can conclude that there is a significant difference between the population mean scores for the math test and the writing test. (b) What is the point estimate of the difference between the mean scores for the two tests? (Use math score − writing score.) = What are the estimates of the population mean scores for the two tests? Math = Writing = Which test reports the higher mean score? The math test reports a (lower/ higher) mean score than the writing test.
A standardized test consists of three parts: math, writing, and critical reading. Sample data showing the math and writing scores for a sample of 12 students who took the test follow.
| Student | Math | Writing |
|---|---|---|
| 1 | 540 | 474 |
| 2 | 432 | 380 |
| 3 | 528 | 463 |
| 4 | 574 | 612 |
| 5 | 448 | 420 |
| 6 | 502 | 526 |
| 7 | 480 | 424 |
| 8 | 499 | 459 |
| 9 | 610 | 615 |
| 10 | 572 | 535 |
| 11 | 390 | 335 |
| 12 | 593 | 613 |
(a) Use a 0.05 level of significance and test for a difference between the population
Formulate the hypotheses.
H0: μd = 0 ; Ha: μd ≠ 0
H0: μd ≤ 0 ; Ha: μd = 0
H0: μd > 0 ; Ha: μd ≤ 0
H0: μd ≠ 0 ; Ha: μd = 0
H0: μd ≤ 0 Ha: μd > 0
Calculate the test statistic. (Round your answer to three decimal places.) =
Calculate the p-value. (Round your answer to four decimal places.)
p-value =
What is your conclusion?
(A) Do not reject H0. We cannot conclude that there is a significant difference between the population mean scores for the math test and the writing test.
(B) Reject H0. We cannot conclude that there is a significant difference between the population mean scores for the math test and the writing test.
(C) Do not reject H0. We can conclude that there is a significant difference between the population mean scores for the math test and the writing test.
(D) Reject H0. We can conclude that there is a significant difference between the population mean scores for the math test and the writing test.
(b) What is the point estimate of the difference between the mean scores for the two tests? (Use math score − writing score.)
=
What are the estimates of the population mean scores for the two tests?
Math =
Writing =
Which test reports the higher mean score?
The math test reports a (lower/ higher) mean score than the writing test.
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