2) (13pt) The Scholastic Aptitude Test (SAT) contains three sections: critical r

Question

2) (13pt) The Scholastic Aptitude Test (SAT) contains three sections: critical reading, mathematics and writing. Each part is scored on a 500-point scale. Information on test scores for the 2017 version of SAT is available at the College Board website. A sample of SAT scores for 5 students follow: SAT scores 2017 Student Reading458 Math Writing 456 454 460 455 457 13.8 459 460 458 455 458 14.7 455 461 458 458 459 60.3 45 Sample Variance a. (10pt)You are hired as statistician to test whether there are any differences among the three sections of the SAT, allowing for 10% error. (3pt) The level of difficulty for all the three sections of the SAT, measured by the score, are supposed to be the same. Do you agree with this after the results of the test? WHY? b.

Explanation / Answer

Since the allowed error rate is 10% we set 90% as our confidence level

Let's take summary of our data (The solution was done in R, code at the bottom to reporoduce the results)

Since the sample means are so close to each other, we can assume that the tests come from the same population.

To confirm this we do an anova with null hypothesis that all means come from the same population with a significance level of 0.1

The results of the Anova are

F- value = 0.714 with a p-value of 0.509

Since the p-value is much greater tha 0.1 we can safely say that these tests for each subject come from the same population

Since we have established that the tests come from the same population their level of difficulty is also similar according to our anova test

The summary of the anova test is

Df Sum Sq Mean Sq F value Pr(>F)
ind 2 10 5 0.714 0.509
Residuals 12 84 7

# R-code

reading <- c(460, 456, 454, 460, 455)
writing <- c(463, 455, 461, 458, 458)
math <- c(458, 459, 460, 458, 455)
grouped <- data.frame(cbind(reading, math, writing))
summary(grouped)
stacked <- stack(grouped)
anova <- aov(values ~ ind, data = stacked)
summary(anova)

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