In: Statistics and Probability
A standardized testt 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 testt follow.
Student | Math | Writing |
---|---|---|
1 | 540 | 474 |
2 | 432 | 380 |
3 | 528 | 457 |
4 | 574 | 612 |
5 | 448 | 420 |
6 | 502 | 526 |
7 | 480 | 430 |
8 | 499 | 453 |
9 | 610 | 615 |
10 | 572 | 541 |
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?
Reject H0. We can conclude that there is a significant difference between the population mean scores for the math test and the writing test.Reject H0. We cannot conclude that there is a significant difference between the population mean scores for the math test and the writing test. 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.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.
(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?
MathWriting
Which test reports the higher mean score?
The math test reports a ---Select--- (higher or lower) mean score than the writing test.
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a)
H0: μd = 0
Ha: μd ≠ 0
Test statisic = -2.375
P value = 0.0368
Conclusion : 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)
Point estimate difference between two score is mean.
mean of their difference = -26
ESTIMATE of Math test is its its Sample mean = 514
ESTIMATE of Writing test is its sample mean = 488
The math test reports a higher mean score than the writing test.
Detailed solution is given below