From the records of the Department of Education, we discover that matric results for the previous five years were normally distributed, with a mean of 62% and a variance of 168. The education...

From the records of the Department of Education, we discover that matric results for the previous five years were normally distributed, with a mean of 62% and a variance of 168. The education authorities identify 10 schools around the country where they suspect that examination papers were leaked and decide to test whether students from these schools performed better at their examinations (ie through cheating) than would have been expected. They draw a random sample of 150 pupils from these 10 schools and calculate their mean result to be 63.8%.

a) Did pupils from these 10 schools perform better than expected (α = 0.05)?

b) Conduct an analysis on the same data to test the research question of whether the pupils performed differently from expectation (α = 0.05).

c) The two tests result in different conclusions. Explain why.

d) What is the chance of making a Type I error in the above tests?

e) How would the chance of making Type I and Type II errors change if we altered the significance level of the tests to α = 0.01?