Homework SourseThe College Board SAT college entrance exam consists of thre
The College Board SAT college entrance exam consists of three parts: math, writing and critical reading (The World Almanac 2012). Sample data showing the math and writing scores for a sample of twelve students who took the SAT follow.
a. Using a .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? Enter negative values as negative numbers. Round your answer to two decimal places.
What is the p-value? Round your answer to four decimal places.
b. What is the point estimate of the difference between the mean scores for the two tests?
What are the estimates of the population mean scores for the two tests?
Which test reports the higher mean score?
| Math test | |
| Writing test |
Solution
A)
Let group 2 = writing scores
group 1 = math scores
Let ud = u2 - u1.
Formulating the null and alternative hypotheses,
Ho: ud >= 0
Ha: ud < 0
At level of significance = 0.05
As we can see, this is a left tailed test.
Calculating the standard deviation of the differences (third column):
s = 37.05033431
Thus, the standard error of the difference is sD = s/sqrt(n):
sD = 10.69551024
Calculating the mean of the differences (third column):
XD = -25
As t = [XD - uD]/sD, where uD = the hypothesized difference = 0 , then
t = -2.337429391
As df = n - 1 = 11
Thus, the P value is,
p = 0.019675138 [ANSWER, P VALUE]
Thus, we Reject Ho. There is significant difference between math and writing scores. [CONCLUSION]
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b)
Getting the means of the math and writing scores,
Math test: X = 514 [ANSWER]
Writing test: X = 489 [ANSWER]
The math test has a higher mean score.
