Solutions Of Tutorial 12

MAA 161 STATISTICS FOR SCIENCES STUDENTS Solutions of Tutorial 12 1.  0 : Median = 60 (claim)

 1 : Median  60 = 0.05, n = 11, C. V. = 1 Test Value = 4 ( > 1) Therefore do not reject the null hypothesis. There is not enough evidence to reject the claim that the median is 60. Yes, considering the number of tornadoes, the median of 60 is relatively small. 2.  0 : The medication has no effect on weight loss.

 1 : The medication affects weight loss. = 0.05, n = 8, C. V. = 0. A B C D E F G H + + + + + – + + Test value = 1 Since 1 > 0, do not reject the null hypothesis. There is not enough evidence to support the claim that the medication affects weight loss. 3.  0 : M D = 0

1 : M D  0 = 0.05, n = 10, From the table, critical value = 8 -309 31 163 1 208 -31 -22 141 265 -103 D -10 2.5 7 1 8 -2.5 -4 6 9 -5 R   w = 21.5, w = 33.5 w = 21.5 w = 21.5 > 8 (do not reject  0 ) There is no difference in the sample of enrolments from medical schools. 4.  0 : M D = 0

1 : M D  0 -30 8 -2 -73 D -6 2.5 -1 -8 R   w = 33.5, w = 2.5 w = 2.5 From the table, critical value = 3 w = 2.5 < 3 (reject  0 ) There is a difference in the costs.

-10 -4

-32 -7

-8 -2.5

-27 -5

5.  0 : 1   2

 1 : 1   2 Calculator A Rank Calculcator B Rank 4.6 7 3.8 1 5 10 4 2 5.1 11 4.2 3 5.3 13 4.3 4 5.5 14 4.5 5.5 5.6 15 4.5 5.5 5.8 16 4.8 8 6.2 17 4.9 9 6.3 18 5.2 12 R1 = 121 R2 = 50

U 1 = 9(9) + 9(10) / 2 –121 = 5 U 2 = 9(9) + 9(10) /2 – 50 = 76 U=5 Critical value = 14 Since U = 5 < 14, reject  0 . Calculator A operates longer than calculator B on a full battery charge. 6.  0 : The purchases of soft drinks 0 occur at random.

 1 : The null hypothesis is not true. PP CCC P C PP C PPP C P C P CCCC P CC PPPP CC There are 16 runs and this value is between 9 and 22. Hence, do not reject the null hypothesis.