In assessing the 2016-2017 junior class at Bradley University, Dr. Timpe has com

Question

In assessing the 2016-2017 junior class at Bradley University, Dr. Timpe has come to the conclusion that he has either gone soft or the students have become noticeably more capable. His conclusion is primarily based on the class average on his exams, formerly thought to strike terror into the hearts of all junior level Mechanical Engineering students. The data is as follows The 20 students from the current class have performed with an average of 65 pts and a standard deviation of 12 pts. · The 100 students from the previous five years have performed with an average of 63 pts and a standard deviation of 15 pts. s. Approximate the confidence with which Dr. Timpe makes his conclusion Show all work for full credit.

Explanation / Answer

Null HYpothesis : H0 : There is no difference in student's performance.

ALternative Hypothesis : Ha : Dr. Timpe conclusion is correct and there is significant difference in their performance

Sample size n1 = 20

sample mean xnew = 65

sample standard deviation s1 = 12

sample mean for old students xold = 63

sample standard deviation s2 = 15

Pooled standard deviation sp = sqrt [{s12 ( (n1 -1) + s22 (n2 -1) }/ (n1 + n2 -2)]

= sqrt [(19 * 122 + 99 * 152)/ 119] = 14.50

Test statitistic

t = (xnew - xold)/ sp * sqrt (1/n1 + 1/n2)

= (65 - 63)/ 14.50 * sqrt(1/20 + 1/100)

= 2/ 3.5517

= 0.56

so p - value = 0.712

so Dr. Timpe is using 30% confidence interval.

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