The mid-distance running coach, Zdravko Popovich, for the Olympic team of an eastern European country claims that his six-month training program significantly reduces
the average time to complete a 1500-meter run. Five mid-distance runners were randomly selected before they were trained with coach Popovich's six-month training
program and their completion time of 1500-meter run was recorded (in minutes). After six months of training under coach Popovich, the same five runners' 1500 meter run
time was recorded again the results are given below.
The hypotheses being tested are
H
0
:
μ
= 0,
H
a
:
μ
> 0, where
μ
represents the mean of the differences in run time (before – after). Assume that the differences are
Normally distributed.
Let
= Completion time before training - Completion time after training. The sample standard deviation of
is calculated to be 0.228.
Quiz: PRACTICE EXAM 2
11 of 15
3/28/2012 3:49 PM

t
= 1.23
t
= 2.75
t
= 2.81
t
= 8.00
We would not reject the null hypothesis of no difference at the 0.10 level and conclude that
there is significant evidence that the mean completion time before training
is longer than the completion time after training.
We would reject the null hypothesis of no difference at the 0.05 level but not at the 0.01 level. Therefore, we can conclude that there is strong (rather than very strong)
evidence that the mean completion time after training is longer than the completion time before training.
We would reject the null hypothesis of no difference at the 0.05 level but not at the 0.01 level. Therefore, we can conclude that there is strong (rather than very strong)
evidence that the mean completion time before training is longer than the completion time after training.
We would reject the null hypothesis of no difference at the 0.01 level and conclude that there is significant evidence that the mean completion time before training is
longer than the completion time after training.
Question 28: 4 pts
Part
A:
What is the value of the
t
test statistic?
INSTRUCTIONS:
1. Use 4 decimal places in your computations.
2. SHOW YOUR WORK AND IDENTIFY (e.g. circle, underline, etc.) YOUR FINAL ANSWER ON THE WORKSHEET (PROVIDED BY YOUR PROCTOR) OR CREDIT
WILL NOT BE GIVEN.
3. Choose one correct answer below.
A)
t
= 1.23
B)
t
= 2.75
C)
t
= 2.81
D)
t
= 8.00
Part
B:
Determine which of the following statements is true.
INSTRUCTIONS:
1. YOUR WORK IS NOT REQUIRED.
2. WRITE DOWN YOUR ANSWER (e.g. A, B, etc.) ON THE WORKSHEET (PROVIDED BY YOUR PROCTOR).
3. CHOOSE ONE CORRECT ANSWER BELOW.
E)
We would not reject the null hypothesis of no difference at the 0.10 level and conclude that
there is significant evidence that the mean
completion time before training is longer than the completion time after training.
F)
We would reject the null hypothesis of no difference at the 0.05 level but not at the 0.01 level. Therefore, we can conclude that there is strong
(rather than very strong) evidence that the mean completion time after training is longer than the completion time before training.

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