Question

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 Writing Math 540 432 474 374 612 420 526 610 615 SAS 11 12 390 593 335 513 (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. #1 || # OOOOOOOOO A L A HMSO 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 - 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 H. We can conclude that there is a significant difference between the population mean scores for the math test and the writing test. Do not reject H. We cannot conclude that there is a significant difference between the population mean scores for the math test and the writing test. Reject H. 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 Select mean score than the writing test.

Answer 1

(a)

Correct option:

H0: $\mu _{d}=0$

Ha: $\mu _{d}\neq 0$

From the given data, values of d = Math score - Writing scores are got as follows:

d = 66, 58, 71, - 38, 28, - 24, 50, 40, - 5, 31, 55, - 20

From d values, the following statistics are calculated:

n = 12

$\bar{d}$ = 312/12=26

s_d = 38.0956

SE = s_d/$\sqrt{12}$

= 10.9973

Test Statistic is given by:

t = 26/10.9973

= 2.364

ndf = n - 1 = 12 - 1 = 11

By Technology, p - value = 0.0000

Correct option:

Reject H0. We can conclude that there is significant difference between the population mean scores for the maths test and writing test.

(b)
Point estimate of difference between the two tests = 26

Math : 6168/12 = 514

Writing: 5856/12 = 488

The math test reports a higher mean score than the writing test.