QANT 201 Statistical Sampling Theory Final- Fall-2017 1 Question 14) As a teache

Question

QANT 201 Statistical Sampling Theory Final- Fall-2017 1 Question 14) As a teacher, I pay particular attention to the mean and standard deviation of exam scores for my classes. A large standard deviation in test scores concems me because it is an indication that some stu- dents are being left behind during the semester. Suppose I want to investigate if having students work in groups reduces the grade variability when compared with a more traditional lecture format. So, in my 10:00 A.M. class, I rely primarily on lectures, whereas in my 11:00 A.M. class, the students spend more time solving problems in groups. I collected the following data after the first exam. 10:00 A.M. Class 86 85 96 83 86 89 89 79 75 11:00 A.M. Class 90 89 76 73 90 88 84 78 86 a. Using 0.01, determine if the 11:00 AM.class experienced less variability in its eam scores than the 10:00 A.M. class did. b. Verlfty your results using Excel. c. Interpret the p-value.

Explanation / Answer

a)
Below are the null and alternate hypothesis
H0: sigma1^2 = sigma2^2
H1: sigma1^2 > sigma2^2

s1^2 = 51.34444
s2^2 = 37.8222

Test statistics, F = s1^2/s2^2 = 1.3575

p-value = 0.3281

b)

Excel output:

c)

As p-value is greater than the significance level of 0.01, we fail to reject null hypothesis.

This means there are not sufficient evidence ot conclude that Class 11.00 AM has less variability than class 10.00 AM

F-Test Two-Sample for Variances 10:00 AM 11:00 AM Mean 86.7 83.6 Variance 51.34444444 37.82222222 Observations 10 10 df 9 9 F 1.357520564 P(F<=f) one-tail 0.328117913 F Critical one-tail 5.351128861

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