Solutions Of Tutorial 11

MAA 161 STATISTICS FOR SCIENCES STUDENTS Solutions of Tutorial 11 1. Let X be the number of the heads obtained when the three coins are tossed H 0 : X~B(3, 0.5)

H 1 : This is not the case Use  2 distribution. When  = 0.05 with df = 3, the critical value of  2 is 7.815 0

3

 3  1   1   X  0        0.125  0  2   2  2

 3  1  1   X  1       0.375  1  2  2  2

 3  1   1   X  2        0.375  2  2   2  3

0

 3  1   1   X  3        0.125  3  2   2  No. of heads

Oi

Pi

Ei

0 1 2 3

3 10 17 42

0.125 0.375 0.375 0.125

9 27 27 9

Oi  Ei 2 Ei 4 10.7037 3.7037 121 2   139.407

Since 139.407 > 70815, reject H 0 . We conclude that the coins are not balanced.

2. H 0 : The way people obtain information is independent

H 1 : This way people obtain information is not independent Use  2 distribution. When  = 0.05 with df = 2, the critical value of  2 is 5.991 High School College Total

Television 159 (139.5) 27(46.5) 186

Newspaper 90(99) 42(33) 132

Other Sources 51(61.5) 31(20.5) 82

Total 300 100 400

 2 = 21.3467 Since 21.3467 > 5.991, reject H 0 We conclude that the way people obtain information is not independent.

3. H 0 : The claim that the proportions of those are willing to participate are equal.

H 1 : The claim that the proportions of those are willing to participate are not equal. Use  2 distribution. When  = 0.01 with df = 2, the critical value of  2 is 9.210 Will participate Will not participate Total

Mall A 52 (44.3333) 40 (47.6667) 92

Mall B 45 (44.3333) 47 (47.6667) 92

Mall C 36 (44.3333) 56 (47.6667) 92

 2 = 5.6016 Since 5.6016 <9.210, do not reject H 0 We conclude that the claim that the proportion of those who are willing to participate are equal.

Total 133 143 276