The College Board SAT college entrance test consists of three parts: math, writi

Question

The College Board SAT college entrance test 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. 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. Enter negative values as negative numbers. What is the test statistic? Round your answer to two decimal places.

What is the p-value? Use z-table. Round your answer to four decimal places.

Explanation / Answer

The College Board SAT college entrance test consists of three parts: math, writing and critical reading (The World Almanac 2012).

Here we have to test the hypothesis that,

H0 : mu1 = mu2 Vs H1 : mu1 not= mu2

where mu1 and mu2 are two population means for math and writing respectively.

Assume alpha = level of significance = 0.05

Here sample size is too small and population standard deviation is unknown so we use two sample t test.

We can test this hypothesis by using MINITAB.

steps :

ENTER data into MINITAB sheet --> STat --> Basic statistics --> 2-Sample t --> Samples in different columns --> First : select math data --> Second :select writing data --> Click on assume equal variances --> Options -->Confidence level : 95.0 --> Test difference : 0.0 --> ALternative : not equal --> ok --> ok

————— 27-11-2017 20:48:11 ————————————————————

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Two-Sample T-Test and CI: math, writing

Two-sample T for math vs writing

N Mean StDev SE Mean
math 12 514.0 68.3 20
writing 12 489.0 93.5 27

Difference = mu math - mu writing
Estimate for difference: 25.0
95% CI for difference: (-44.3, 94.3)
T-Test of difference = 0 (vs not =): T-Value = 0.75 P-Value = 0.462 DF = 22
Both use Pooled StDev = 81.8

Test statistic = 0.75

P-value = 0.462

P-value > alpha

Accept H0 at 5% level of significance.

Conclusion : There is sufficient evidence to say that two population means are equal.

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