STATISTICS 3N03/3J04 – TEST #3B – 2006-11-30

Aids permitted: any calculators, any tables and one sheet of notes (8.5" x 11", one side only).

1. Analyze the following two data sets with appropriate graphics and P-values. State your assumptions and your conclusions. Wherever possible, assess the validity of your assumptions. [32 marks]

(a) The following data give energy intake and expenditure in MJ/day for 7 soccer players. Can you conclude that there is a difference between intake and expenditure? Do the analysis two ways, with and without assuming normality; do your conclusions agree? Which test has the greater power? Which test is the more robust?

Player:           1     2     3     4     5     6     7
Expenditure:      14.4  12.1  14.3  14.2  15.2  15.5  17.8
Intake:           14.4  9.2   11.8  11.6  12.7  15.0  16.3

(b) 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?

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

2. Consider the data in Q1b. If you did a two-sided test at the 1% level of significance and the true difference in mean bacteria count was 2 colonies/ft³, what would be the probability of a Type II error? [5 marks]
3. Give the full name and three interesting facts about the chemist who invented the t-distribution. [3 marks]