An instructor believes that students do not retain as much information from a le

Question

An instructor believes that students do not retain as much information from a lecture on a Friday compared to a Monday. To test this belief, the instructor teaches a small sample of college students some preselected material from a single topic on statistics on a Friday and on a Monday. All students received a test on the material. The differences in test scores for material taught on Friday minus Monday are listed in the following table. Difference Scores (Friday Monday) +6.3 +3.4 1.5 +1.0 +4.4

(a) Find the confidence limits at a 95% CI for these related samples. (Round your answers to two decimal places.)

Explanation / Answer

(a)

The mean of difference scores is (6.3 +3.4 1.5 +1.0 +4.4) / 5 = 2.72

The standard deviation of difference scores , SD = sqrt [ ((di - d)2 / (n - 1) ]   (where di are the differences and d is the mean)

= sqrt[(6.3 - 2.72)^2 + (3.4 - 2.72)^2 + (1.5 - 2.72)^2 +(1.0 - 2.72)^2 +(4.4 - 2.72)^2 / 4] = 3.04

Standard error of difference scores = SD / sqrt(n)

= 3.04 / sqrt(5) = 1.36

Z-value at 95% confidence interval is 1.96

95% CI of difference scores = (2.72 - 1.96*1.36, 2.72 + 1.96*1.36)

= (0.05, 5.39)

So, the confidence limits at a 95% CI are (0.05, 5.39)

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