[Solved] MAST30025 Lab 10

1. Consider again the data from Question 5 from the Week 8 lab. In a manufacturing plant, filtersare used to remove pollutants. We are interested in comparing the lifespan of 5 different types of filters. Six filters of each type are tested, and the time to failure in hours is given in the dataset filters (on the website, in csv format).
   • Calculate s².
   • Calculate a 95% confidence interval for the difference in lifespan between filter types 3 and 4.
   • Show that the hypothesis that the filters all have the same lifespan is testable.
   • Test this hypothesis, using matrix theory.
   • Test the same hypothesis using the linearHypothesis function from the car
2. Derive a formula for a prediction interval for t^T in the less than full rank model.
3. Consider a one-way classification model with three levels. To test ₁ = ₂ = ₃ we could use either of the following matrices:

.

Show that the test statistics formed using these two matrices are the same.

Hint: find A such that AC₁ = C₂.

4. An industrial psychologist is investigating absenteeism among production-line workers, based ondifferent types of work hours: (1) 4-day week with a 10-hour day, (2) 5-day week with a flexible 8hour day, and (3) 5-day week with a structured 8-hour day. A study is conducted and the following data obtained of the average number of days missed:

Work plan

Number100 85 90

They also find s² = 110.15.

• Test the hypothesis that the work plan has no effect on the absenteeism.
• Test the hypothesis that work plans 1 and 3 have the same rate of absenteeism.