Question

QUESTION 8

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.

   What are the assumptions the animal scientists should make?

   	a.	The standard deviation of the differences in pairs of data must be known.
   	b.	The differences in pairs of data must come from a population with Normal distribution.
   	c.	The differences in pairs of data must be IID.
   	d.	b and c

Answer 1

Solution:

Given that, the animal scientists at the North Pole train the reindeer to improve their take-off speed. the data on each of the current reindeer was timed in the 200-yard dash before and after using the device is given.

To test the hypothesis the animal scientist should use paired sample t - test, the assumptions of the paired sample t-test is given as:

1) the differences in pairs of data must come from a population with Normal distribution.

2) The differences in pairs of data must be IID.

Therefore, the animal scientist should make these two assumptions.

Hence, option d is correct.