B218 BS08 Worksheet 20130924
PBL PROBLEM WORKSHEET Title of Problem:
Judges at the Olympics
Module:
B218 Business Statistics
1. A running coach is researching how the pace of runners changes during the course of a race.
a. He takes a simple random sample of 20 athletes running an 800m race. The 800m race consists of two laps round a 400m track. What statistical test should he perform to determine whether there is a difference between population average completion times for the first lap and the last lap?
b. He takes another simple random sample of 20 athletes running a 1200m race. The 1200m race consists of three laps round a 400m track. How many pairs of laps would he have to test in order to determine whether there are any differences between population average completion times for the three laps? 3
c. He takes another simple random sample of 20 athletes running a 10000m race. The 10000m race consists of 25 laps round a 400m track. How many pairs of laps would he have to test in order to determine whether there are any differences between population average completion times for the 25 laps? 300
d. Suppose that the statistical tests he conducts are performed at the 5% significance level. For each test he performs, there is a 5% chance of incorrectly concluding that there is a difference between population average completion times; i.e., there is a 5% chance of making a Type I error for each pairwise test performed.
Complete the following table to determine how the probability of making a Type I error changes as the number of laps in the race increases. One example has been done for your reference.
2
1
0.95
0.05
3
3
0.857375
0.142625
4
6
0.735091891
0.264908109
5
10
0.598736939
0.401263061
6
15
0.46329123
0.53670877
7
21
0.340561626
0.659438374
8
28
0.237826885
0.762173115
9
36
0.157779215
0.842220785
10
45
0.099440257
0.900559743
11
55
0.059538555
0.940461445
12
66
0.033865536
0.966134464
13
78
0.018299584
0.981700416
14
91
0.009393946
0.990606054
15
105
0.004581193
Judges at the Olympics
Module:
B218 Business Statistics
1. A running coach is researching how the pace of runners changes during the course of a race.
a. He takes a simple random sample of 20 athletes running an 800m race. The 800m race consists of two laps round a 400m track. What statistical test should he perform to determine whether there is a difference between population average completion times for the first lap and the last lap?
b. He takes another simple random sample of 20 athletes running a 1200m race. The 1200m race consists of three laps round a 400m track. How many pairs of laps would he have to test in order to determine whether there are any differences between population average completion times for the three laps? 3
c. He takes another simple random sample of 20 athletes running a 10000m race. The 10000m race consists of 25 laps round a 400m track. How many pairs of laps would he have to test in order to determine whether there are any differences between population average completion times for the 25 laps? 300
d. Suppose that the statistical tests he conducts are performed at the 5% significance level. For each test he performs, there is a 5% chance of incorrectly concluding that there is a difference between population average completion times; i.e., there is a 5% chance of making a Type I error for each pairwise test performed.
Complete the following table to determine how the probability of making a Type I error changes as the number of laps in the race increases. One example has been done for your reference.
2
1
0.95
0.05
3
3
0.857375
0.142625
4
6
0.735091891
0.264908109
5
10
0.598736939
0.401263061
6
15
0.46329123
0.53670877
7
21
0.340561626
0.659438374
8
28
0.237826885
0.762173115
9
36
0.157779215
0.842220785
10
45
0.099440257
0.900559743
11
55
0.059538555
0.940461445
12
66
0.033865536
0.966134464
13
78
0.018299584
0.981700416
14
91
0.009393946
0.990606054
15
105
0.004581193