Question 8 Background Where do you seat during lecture? Research shows that, in

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Question 8 Background Where do you seat during lecture? Research shows that, in all subject areas, students who sit in the front of the classroom tend to achieve higher average exam scores. These findings occur even when students are assigned to these seats by their instructor, which indicates that it is not simply due to the fact that more motivated students tend to sit in the front. To examine this claim, we take a random sample of 14 Exam scores from students who sit in the front during lectures (group 1) and compare them to the Exam scores of 16 randomly selected students who sit in the back during lectures (group 2). A 5% significance level will be used to perform the following test: H0: ront-uback-0 against Ha: front-uback > O. The following is the R output on the data. Numerical summaries mean sd se (mean score:n front 57.71 23.36 6.2432 back 14 16 43.78 21.805.45 Pooled t-test Two Sample t-test data: score by location t= 1.6889, df= 28, p-value = 0.0512 alternative hypothesis: true difference in means is greater than 0 sample estimates: mean in group front mean in group back 57.71 43.78 Question 8 Subquestions Compute the estimate of the common population standard deviation of exam scores point(s) 1.56 points 22.58 points 22.5377 points 22.9753 points 8.b If there is no difference in the population mean exam scores for the two types of students (those that sit in the front versus those that sit in the back), what is the distribution of the test statistic? point(s) N(13.93, 8.2874) t(13) t(28)

Explanation / Answer

H0: 1 – 2 = 0

H1: 1 – 2 > 0

Sp^2=(n1-1)*S1^2+(n2-1)*S2^2/(n1-1)+(n2-1)

=(14-1)*23.36^2+(16-1)*21.80^2/(14-1)+(16-1)

=507.9487

    Sp=22.5377

tSTAT=(X1-X2)-(1-2)/Sp^2(1/n1+1/n2)

=(57.71-43.78)-0/507.9487(1/14+1/16)

=1.68889

Please find below the answers: -

8.a)

22.5377

8.b)

t(28)

8.c)

1.68889

8.d)

5.12

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