The duration of the test is 1 hour.
Any calculators, photocopies of the
Tables from the textbook,
and one sheet of notes (8.5" x 11", one side only) are permitted.
You are manufacturing an auto part that is supposed to weigh 2.5 kg; however, as long as the weight is between 2.4 and 2.6 kg it will be within specifications. Your weigh scale is unbiased but has a standard deviation of 0.2 kg. If you weigh a part 4 times independently and do a two-sided 5% test, show that the probability of accepting a part that does not meet specifications could be as high as 83%. If you wanted to reduce this probability to 10%, how many times would you have to weigh the part?
The following data give energy intake and expenditure in MJ/day for 7 soccer players. Give a P-value to test whether there is a significant difference between intake and expenditure. State your assumptions and your conclusions. Where possible, test your assumptions. Give an appropriate graph.
Player: 1 2 3 4 5 6 7
Expenditure: 14.4 12.1 14.3 14.2 15.2 15.5 17.8
Intake: 14.6 9.2 11.8 11.6 12.7 15.0 16.3
Analyse the data of Question 2 using a non-parametric test. State your assumptions and your conclusions.
The following data give airborne bacteria count (colonies/ft3) for samples from 8 carpeted hospital rooms and 8 uncarpeted hospital rooms. Does there appear to be a difference in the true average bacteria counts between carpeted and uncarpeted rooms? Support your conclusion with a P-value. State your assumptions and your conclusions. Where possible, test your assumptions. Give an appropriate graph.
Carpeted: 11.8 8.2 7.1 13.0 10.8 10.1 14.6 14.0
Uncarpeted: 12.1 8.3 3.8 7.2 12.0 11.1 10.1 13.7