Question

QUESTION 10

1. During the off-season (January – October), animal scientists at the North Pole train the reindeer to improve their take-off speed. During the most recent off-season, a new training device was used to improve the average time required for reindeer to sprint 200 yards. Each of the current reindeer was timed in the 200-yard dash before and after using the device. The results (in sec) are given in the table below.

   Reindeer	Time Before Training	Time After Training
   1	8.5	7.5
   2	8.62	8.42
   3	7.98	7.65
   4	8.41	7.89
   5	9.15	9.01
   6	7.45	6.69
   7	8.55	7.98
   8	7.11	6.88
   9	9.02	8.56

   Using this data, the animal scientists wish to test the following hypotheses using a level of significance of 0.05.

   Note that mu1 denotes the average time required for an untrained reindeer to sprint 200 yards and mu2 denotes the average time required for a trained reindeer to sprint 200 yards.

   Identify the critical region.

Answer 1

$H_{0}:\mu_{1}\geq \mu_{2}\:vs\:H_{1}:\mu_{1}<\mu_{2}$

The output of the paired t test is:

Paired T-Test and CI: Before, After

Paired T for Before - After

N Mean StDev SE Mean
Before 9 8.310 0.680 0.227
After 9 7.842 0.762 0.254
Difference 9 0.4678 0.2821 0.0940

95% upper bound for mean difference: 0.6426
T-Test of mean difference = 0 (vs < 0): T-Value = 4.97 P-Value = 0.999

Critical region =

$t<t_{\frac{0.05}{2};16}=2.12$

Since observed t does not fall in the critical region so we fail to reject the null hypothesis.

Based on this data, the new training device doesn't seem to improve the take-off speed of the reindeer