Question

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. 1 Reindeer Time Before Training Time After Training 8.19 7.83 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. Ho: H1 = 42 Hi: Hi>H2 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. a) Compute the test statistic. b) Identify the critical region. Ho: H1 = 42 Hi: H1>H2 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. Suppose data (time before training, time after training) are collected from 13 different reindeer and the resulting test statistic is -2. c) You fail to reject the null hypothesis. True False 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. Suppose data (time before training, time after training) are collected from 9 different reindeer and the resulting test statistic is zero. d) Compute the P-value for this test. 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. Suppose data (time before training, time after training) are collected from 9 different reindeer and the resulting test statistic is 1. e) Compute the P-value for this test. Note that mu 1 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. Suppose data (time before training, time after training) are collected from 9 different reindeer and the result are given below, Õ =0.22. SD=0.88 where D denotes the difference between each pair of data. f) Compute the lower bound of the confidence interval that is relevant to this problem.

Answer 1

1 During the off-season, animal scientists at the North Pole train the reindeer to improve their take-off speed. The animal scientists wish to test the hypothesis He: uz Hi u > M2 la denotes the an average time required for an untrained reindeer to sprint 200 yards and M2 denotes the avera age time required for a trained reindeer to sprint Mi 200 yards. +9.02 8.2755 8.19+ 8.62 + - a) Xi g + 8.56 11 7.8788 7.83+ 8.42 + X2 - co XD = 8.2755 - 7.8788 = 0.3967 D = Time before training Time after training 0:36, Oud, 0:33, 0.52, 0114, 0.76, 0.57, 0-23, 0.46 S. 1 £(D - B)2 0-36-0.396 In- 8 +---+ (0.46– 0.3967) 2 2

So So the 0.1998) test statistic will be I-llo So TS = tn-i Jn 0.3967 5.95615 0.19981 Ј9 So the test statistic is 5.98615. b) The critical region will be, to 1.860. 8,0.05 So the critical will be [1.860,0). () The the test statistic lies in the rejection region. to reject the null hypothesis So the given statement is false d) The p-value for this test will be p-value = t > 5.95615 0.00017 we will pl 8 The p-value at sl. lenel of significance is 0.00017.