Question

1. The College Board SAT college entrance 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 SAT follow

Student	Math	Writing
1	540	474
2	432	380
3	528	463
4	574	612
5	448	420
6	502	526
7	480	430
8	499	459
9	610	615
10	572	541
11	390	335
12	593	613

Use 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. What is the p-value and what is your conclusion?

Answer 1

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AS FOR GIVEN DATA..

a) We want to see if the population mean for math scores is different from that of writing scores, ie

we want to test

     

, where & denotes the population mean of math and writing scores respectively.

The test results is as following :-

The p-value of the test is 0.4630 which is greater than level of significance 0.05. Also the value of t-Stat(observed value of the test statistic) is less than 2.0860, which is the critical value. Hence we do not have enough evidence to reject and conclude that the population mean for math scores is not significantly different from that of writing scores.

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