In: Statistics and Probability
A standardized exam 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 exam follow.
Student | Math | Writing |
---|---|---|
1 | 540 | 474 |
2 | 432 | 380 |
3 | 528 | 457 |
4 | 574 | 606 |
5 | 448 | 414 |
6 | 502 | 526 |
7 | 480 | 430 |
8 | 499 | 459 |
9 | 610 | 615 |
10 | 572 | 541 |
11 | 390 | 329 |
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 =
(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
Student | Math | Writing | Difference(d) |
1 | 540 | 474 | 66 |
2 | 432 | 380 | 52 |
3 | 528 | 457 | 71 |
4 | 574 | 606 | -32 |
5 | 448 | 414 | 34 |
6 | 502 | 526 | -24 |
7 | 480 | 430 | 50 |
8 | 499 | 459 | 40 |
9 | 610 | 615 | -5 |
10 | 572 | 541 | 31 |
11 | 390 | 329 | 61 |
12 | 593 | 613 | -20 |
Total | 324 |
a)
The null and alternative hypothesis is
H0: μd = 0
Ha: μd ≠ 0
Level of significance = 0.05
Sample size = n = 12
Sample mean of difference = = 27
Sample standard deviation of difference = = 37.3144
Test statistic is
Degrees of freedom = n - 1 = 12 - 1 = 11
P-value = 2*P(T > 2.51) = 0.0292
b)
The point estimate of the difference between the mean scores for the two tests = Sample mean of difference = = 27
What are the estimates of the population mean scores for the two tests?
Math = = 514
Writing = = 487