Question

In: Statistics and Probability

A standardized exam consists of three parts: math, writing, and critical reading. Sample data showing the...

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

Solutions

Expert Solution

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


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