Question

a)

A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. Final examination scores from a random sample of students enrolled today and from a random sample of students enrolled five years ago were selected. You are given the following information. Today 82 Five Years Ago 88 62 112.5 54 n 45 36 What conclusion can be reached about the difference in the average final examination scores between the two classes? (Use a 01 level of significance.) There is a statistically significant difference in the average final examination scores between the two classes. There is no statistically significant difference in the average final examination scores between the two classes. It is impossible to make a decision on the basis of the information given. There is a difference, but it is not significant.

b)

Answer 1

ay Today bolun. m = 1=45 a = B2 0,2 = 112.5 Five years ago n₂ = 36 d = 88, 97² = 54 Ho: 4,= M2 Vs Hii Mi 7 42 Here population standard deviation are known so we use two Sample Z-test. Test Statistic (ä, - ) +02 n nz 82-88 - 6 2 112.5 45 + 54 36 Z=-3 d = 0.01 ) 2/2=0.005 Za = 2.58 (two sided) bince IZI ? Zdi Reject Ho at 2=0.0) Ans. =) There is a statistically significant in the average Binal examination scores between the two classes. 1 1 2. by =) Male ni=64 x = 44 0,2 128 Female = n2 = 36 M 2 = 41 72 confidence interval for difference between the means ol two popun is (2,-2) I E ; where E=margin of error d=0.01 = Za=2.58 ::E= Z2 + = 2.58 k 128 72 = 2.58*2 = 5.16 64 36 0,2 022 + n2 -2.16 -2.15 upper Limit Lower Limil= (2,-2) -E = (44-41) - 5.16 (ł, -2) + E = (44-41) 45.16 Ans. - 2.15 to 8.15 8.15