Chapter 15
15.1.1, .2, .3, .2, .2
At least one is not equal to its specified value.
Cell i
1 24300(.1) = 30-6 1.20
2 64300(.2) = 60 4.27
3 84300(.3) = 90 -6.40
4 72300(.2) = 60 122.40
5 56300(.2) = 60 -4 .27
Total 300 300 = 4.54
Rejection region: 13.3
= 4.54, p-value = .3386. There is not enough evidence to infer that at least one is not equal to its specified value.
15.2.1, .2, .3, .2, .2
At least one is not equal to its specified value.
Cell i
1 12150(.1) = 15 -3 .60
2 32150(.2) = 30 2 .13
3 42150(.3) = 45 -3 .20
4 36150(.2) = 30 6 1.20
5 28150(.2) = 30 -2 .13
Total 150 150 = 2.26
Rejection region: 13.3
= 2.26, p-value = .6868. There is not enough evidence to infer that at least one is not equal to its specified value.
15.3.1, .2, .3, .2, .2
At least one is not equal to its specified value.
Cell i
1 675(.1) = 7.5 -1.5 .30
2 1675(.2) = 15 1 .07
3 2175(.3) = 22.5 -1.5 .10
4 1875(.2) = 15 3 .60
5 1470(.2) = 15 -1 .07
Total 75 75 = 1.14
Rejection region: 13.3
= 1.14, p-value = .8889. There is not enough evidence to infer that at least one is not equal to its specified value.
15.4 Thestatistic decreases.
15.5.3, .3, .2, .2
At least one is not equal to its specified value.
Cell i
1 38150(.3) = 45 -7 1.09
2 50150(.3) = 45 5 0.56
3 38150(.2) = 30 8 2.13
4 24150(.2) = 30 -6 1.20
Total 150 150 = 4.98
Rejection region: 7.81
= 4.98, p-value = .1734. There is not enough evidence to infer that at least one is not equal to its specified value.
15.6.3, .3, .2, .2
At least one is not equal to its specified value.
Cell i
1 76300(.3) = 90 -14 2.18
2 100300(.3) = 90 10 1.11
3 76300(.2) = 60 16 4.27
4 48300(.2) = 60 -12 2.40
Total 300 300 = 9.96
Rejection region: 7.81
= 9.96, p-value = .0189. There is enough evidence to infer that at least one is not equal to its specified value.
15.7.2, .2, .2, .2, .2
At least one is not equal to its specified value.
Cell i
1 28100(.2) = 20 8 3.20
2 17100(.2) = 20 -3 0.45
3 19100(.2) = 20 -1 0.05
4 17100(.2) = 20 -3 0.45
5 19100(.2) = 20 -1 0.05
Total 100 100 = 4.20
Rejection region: 7.78
= 4.20, p-value = .3796. There is not enough evidence to infer that at least one is not equal to its specified value.
15.8.15, .40, .35, .10
At least one is not equal to its specified value.
Cell i
1 41 233(.15) = 34.95 6.05 1.05
2 107 233(.40) = 93.20 13.80 2.04
3 66 233(.35) = 81.55 -15.55 2.97
4 19 233(.10) = 23.30 -4.30 0.79
Total 233 233 = 6.85
Rejection region: 7.81
= 6.85, p-value = .0769. There is not enough evidence to infer that at least oneis not equal to its specified value.
15.91/6, 1/6, 1/6, 1/6, 1/6, 1/6
At least one is not equal to its specified value.
Cell i
1 114600(1/6) = 100 14 1.96
2 92600(1/6) = 100 -8 0.64
3 84600(1/6) = 100 -16 2.56
4 101600(1/6) = 100 1 0.01
5 107600(1/6) = 100 7 0.49
6 102600(1/6) = 100 2 0.04
Total 600 600 = 5.70
Rejection region: 11.1
= 5.70, p-value = .3365. There is not enough evidence to infer that the die is not fair.
15.10.05, .25 .40, .25 .05
At least one is not equal to its specified value.
Cell i
1 11 150(.05) = 7.5 3.5 1.63
2 32 150(.25) = 37.5 -5.5 0.81
3 62 150(.40) = 60.0 2.0 0.07
4 29 150(.25) = 37.5 -8.5 1.93
5 16 150(.05) = 7.5 8.5 9.63
Total 150 150 = 14.07
Rejection region: 7.78
= 14.07, p-value = .0071. There is enough evidence to infer that grades are distributed differently from grades in the past.
15.11.2, .2 .2, .2 .2
At least one is not equal to its specified value.
Cell i
1 8 25(.2) = 5.0 3.0 1.80
2 4 25(.2) = 5.0 -1.0 0.20
3 3 25(.2) = 5.0 -2.0 0.80
4 8 25(.2) = 5.0 3.0 1.80
5 2 25(.2) = 5.0 -3.0 1.80
Total 25 25 = 6.40
Rejection region: 9.49
= 6.40, p-value = .1712. There is not enough evidence to infer that the professor does not randomly distribute the correct answer over the five choices.
15.12.72, .15, .10, .03
At least one is not equal to its specified value.
Cell i
1 159 250(.72) = 180.0 -21.0 2.45
2 28 250(.15) = 37.5 -9.5 2.41
3 47 250(.10) = 25.0 22.0 19.36
4 16 250(.03) = 7.5 8.5 9.63
Total 250 250 = 33.85
Rejection region: 7.81
=33.85, p-value = 0. There is enough evidence to infer that the aging schedule has changed.
15.13.15, .25, .40, .20
At least one is not equal to its specified value.
Cell i
1 36 250(.15) = 29.55 6.45 1.41
2 58 250(.25) = 49.25 8.75 1.55
3 74 250(.40) = 78.80 -4.80 0.29
4 29 250(.20) = 39.40 -10.40 2.75
Total 197 197 = 6.00
Rejection region: 7.81
= 6.00, p-value= .1116. There is not enough evidence to infer that certain sizes of cars are involved in a higher than expected percentage of accidents.
15.14.31, .51, .18
At least one is not equal to its specified value.
Cell i
1 408 1200(.31) = 372 36 3.48
2 571 1200(.51) = 612 -41 2.75
3 221 1200(.18) = 216 5 0.12
Total1200 1200 = 6.35
Rejection region: 4.61
= 6.35, p-value = .0419. There is enough evidence to infer that voter support has changed since the election.
15.15.05, .07, .04, .84
At least one is not equal to its specified value.
Cell i
1 19 250(.05) = 12.5 6.5 3.38
2 23 250(.07) = 17.5 5.5 1.73
3 14 250(.04) = 10.0 4.0 1.60
4 194 250(.84) = 210.0 -16.0 1.22
Total 250 250 = 7.93
Rejection region: 7.81
= 7.93, p-value = .0475. There is enough evidence to infer that the reported side effects of the placebo differ from that of the cold remedy.
15.16.23, .40, .15, .22
At least one is not equal to its specified value.
Cell i
1 63 320(.23) = 73.6 -10.61.53
2 125 320(.40) = 128.0 -3.00.07
3 45 320(.15) = 48.0 -3.00.19
4 87 320(.22) = 70.4 16.63.91
Total 320 320 = 5.70
Rejection region: 7.81
= 5.70, p-value = .1272.There is not enough evidence to infer that there has been a change in proportions.
15.17 The two variables are independent
The two variables are dependent
Cell i
1 28 96(84)/188 = 42.89 -14.89 5.17
2 68 96(104)/188 = 53.11 14.89 4.17
3 56 92(84)/188 = 41.11 14.89 5.40
4 36 92(104)/188 = 50.89 -14.89 4.36
Total 188 188 = 19.10
Rejection region: 3.84
= 19.10, p-value = 0. There is enough evidence to infer that the two variables are dependent.
15.18 The two variables are independent
The two variables are dependent
Cell i
1 14 48(42)/188 = 21.45 -7.45 2.59
2 34 48(52)/188 = 26.55 7.45 2.09
3 28 46(42)/188 = 20.55 7.45 2.70
4 18 46(52)/188 = 25.45 -7.45 2.18
Total 94 94 = 9.56
Rejection region: 3.84
= 9.56, p-value = .0020. There is enough evidence to infer that the two classifications L and M are dependent.
15.19 The two variables are independent
The two variables are dependent
Cell i
1 7 24(21)/188 = 10.72 -3.72 1.29
2 17 24(26)/188 = 13.28 3.72 1.04
3 14 23(21)/188 = 10.28 3.72 1.35
4 9 23(26)/188 = 12.72 -3.72 1.09
Total 47 47 = 4.77
Rejection region: 3.84
= 4.77, p-value = .0289. There is enough evidence to infer that the two classifications L and M are dependent.
15.20 Thestatistic decreases.
15.21 The two variables are independent
The two variables are dependent
Cell i
1 40 120(70)/250 = 33.60 6.40 1.22
2 32 120(80)/250 = 38.40 - 6.40 1.07
3 48 120(100)/250 = 48.00 0 0.00
4 30 130(70)/250 = 36.40 -6.40 1.13
5 48 130(80)/250 = 41.60 6.40 0.99
6 52 130(100)/250 = 52.00 0 0.00
Total 250 250 = 4.41
Rejection region: 4.61
= 4.41, p-value = .1110. There is not enough evidence to infer that the two classifications R and C are dependent.
15.22 The two variables (responses and employee group) are independent
The two variables are dependent
Cell i
1 67 110(130)/200 = 71.50 -4.500.28
2 32 110(50)/200 = 27.50 4.50 0.74
3 11 110(20)/200 = 11.00 0 0.00
4 63 90(130)/200 = 58.50 4.50 0.35
5 18 90(50)/200 = 22.50 -4.50 0.90
6 9 90(20)/200 = 9.00 0 0.00
Total 200 200 = 2.27
Rejection region: 5.99
= 2.27, p-value = .3221. There is not enough evidence to infer that responses differ among the three groups of employees.
15.23 The two variables (shirt condition and shift) are independent
The two variables are dependent
Cell i
1240570(250)/600 = 237.52.5.03
2191570(200)/600 = 190.01.0 .01
3139570(150)/600 = 142.5-3.5 .09
410 30(250)/600 = 12.5 -2.5 .50
5 9 30(200)/600 = 10.0 -1.0 10
61130(150)/600 = 7.5 3.5 1.63
Total 600 600 = 2.36
Rejection region: 5.99
= 2.36, p-value = .3087. There is not enough evidence to infer that there are differences in quality among the three shifts.
15.24 The two variables economic option and political affiliation) are independent
The two variables are dependent
Cell i
1101444(331)/1000 = 146.96-45.96 14.376
2282444(557)/1000 = 233.9948.01 9.852
361444(142)/1000 = 63.05-2.05 0.067
438 130(331)/1000 = 43.03 -5.03 0.588
5 67 130(557)/1000 = 68.51 -1.51 0.033
625130(142)/1000 = 18.466.54 2.317
7131250(331)/1000 = 82.7548.25 28.134
888250(557)/1000 = 131.75-43.75 14.528
931 250(142)/1000 = 35.50 -4.50 0.570
10 61 176(331)/1000 = 58.26 2.74 0.129
11 90 176(557)/1000 = 92.75-2.75 0.082
1225176(142)/1000 = 24.99 0.01 0.000
Total 1000 1000 = 70.675
Rejection region: 16.8
= 70.675, p-value = 0. There is sufficient evidence to infer that political affiliation affects support for economic options.
15.25 The two variables (inducement and return) are independent
The two variables are dependent
Cell i
180300(200)/1000 = 60206.67
2100300(300)/1000 = 9010 1.11
3120300(500)/1000 = 150-30 6.00
4120 700(200)/1000 = 140 -20 2.86
5 200 700(300)/1000 = 210 -10 0.50
6380700(500)/1000 = 350 30 2.57
Total1000 1000 = 19.71
Rejection region: 5.99
= 19.71, p-value = .0001. There is sufficient evidence to infer that the return rates differ among the different inducements.
15.26 The two variables (newspaper and occupation) are independent
The two variables are dependent
Cell i
127 120(89)/354=30.2-3,2 .33
218120(112)/354=38.0-20.010.50
3 38120(81)/354=27.510.54.05
4 37120(72)/354=24.412.66.50
529108(89)/354=27.21.8.13
643108(112)/354=34.28.82.28
721108(81)/354=24.7-3.7.56
815108(72)/354=22.0-7.02.21
933126(89)/354=31.71.3.06
1051126(112)/354=39.911.13.11
1122126(81)/354=28.8-6.81.62
1220126(72)/354=25.6-5.61.24
Total 354 354 = 32.57
Rejection region: 12.6
= 32.57, p-value = 0. There is sufficient evidence to infer that occupation and newspaper are related.
15.27a The two variables (predicted change and actual change) are independent
The two variables are dependent
Cell i
165129(104)/216 = 62.112.89.13
23987(104)/216 = 41.89-2.89 .20
364129(112)/216 =66.89-2.89 .12
448 87(112)/216 = 45.112.89 .19
Total 216 216 = .64
Rejection region: 2.71
= .64, p-value = .4225. There is not enough evidence to infer that the predicted and actual directions of change are related.
b Ignore what the other investors are doing.
15.28 The two variables (last purchase and second-last purchase) are independent
The two variables are dependent
Cell i
139149(153)/559 = 40.78−1.78.08
236149(134)/559 = 35.72 .280
351149(190)/559 = 50.64 .360
423 149(82)/559 = 21.86 1.14 .06
5 36 134(153)/559 = 36.68−.68 .01
632134(134)/559 = 32.12−.12 0
746134(190)/559 = 45.55.450
820134(82)/559 = 19.66.34 .01
954 194(153)/559 = 53.10 .90 .02
10 46 194(134)/559 = 46.50 −.50 .01
11 65 194(190)/559 = 65.94 −.94.01
1229194(82)/559 = 28.46.54.01
132482(153)/559 = 22.441.56.11
142082(134)/559 = 19.66.34.01
152882(190)/559 = 27.87.130
161082(82)/558= 12.03−2.03.34
Total559559 = .67
Rejection region: 16.9
= .67, p-value = .9999. There is no evidence of a relationship.
15.29 The two variables (education and smoker) are independent
The two variables are dependent
Cell i
13457(460)/1000 = 26.227.782.31
22357(540)/1000 = 30.78-7.78 1.97
3251463(460)/1000 = 212.9838.02 6.79
4212 463(540)/1000 = 250.02 -38.02 5.78
5 159 407(460)/1000 = 187.22 -28.22 4.25
6 248407(540)/1000 = 219.7828.223.62
71673(460)/1000 = 33.58-17.589.20
85773(540)/1000 = 39.4217.58 7.84
Total1000 1000 = 41.77
Rejection region: 7.81
= 41.77, p-value = 0. There is sufficient evidence to infer that the amount of education is a factor in determining whether a smoker will quit.
15.30 The two variables (education and smoker) are independent
The two variables are dependent
Cell i
160121(369)/658 =67.9-7.9.91
223121(116)/658=21.31.7.13
313121(65)/658=12.01.0.09
425121(108)/658=19.95.11.33
565126(369)/658=70.7-5.7.45
619126(116)/658=22.2-3.2.46
714126(65)/658=12.41.6.19
828126(108)/658=20.77.32.59
973132(369)/658=74.0-1.0.01
1026132(116)/658=23.32.7.32
119132(65)/658=13.0-4.01.25
1224132(108)/658=21.72.3.25
136795(369)/658=53.313.73.54
141195(116)/658=16.7-5.71.97
151095(65)/658=9.40.6.04
16795(108)/658=15.6-8.64.74
175796(369)/658=53.83.2.19
181696(116)/658=16.9-.9.05
19996(65)/658=9.5-.5.02
201496(108)/658=15.8-1.8.20
214788(369)/658=49.3-2.3.11
222188(116)/658=15.55.51.94
231088(65)/658=8.71.3.20
241088(108)/658=14.4-4.41.37
Total 658 658 = 22.36
Rejection region: 25.0
= 22.36, p-value = .0988. There is not enough evidence to infer that there is a relationship between an adult’s source of news and his or her heartburn condition.
15.31 The two variables (university and degree) are independent
The two variables are dependent
Cell i
144100(167)/400=41.752.25.12
211100(64)/400=16.00-5.001.56
334100(121)/400=30.253.75.46
411100(48)/400=12.00-1.00.08
552100(167)/400=41.7510.252.52
614100(64)/400=16.00-2.00.25
727100(121)/400=30.25-3.25.35
87100(48)/400=12.00-5.002.08
931100(167)/400=41.75-10.752.77
1027100(64)400=16.0011.007.56
1118100(121)400=/30.25-12.254.96
1224100(48)/400=12.0012.0012.00
1340100(167)/400=41.75-1.75.07
1412100(64)/400=16.00-4.001.00
1542100(121)/400=30.2511.754.56
166100(49)/ 400=12.00-6.003.00
Total 400 400 = 43.36
Rejection region: 16.9
= 43.36, p-value = 0. There is enough evidence to infer that undergraduate degree and the university applied to are related.
15.32 The two variables (results and financial ties) are independent
The two variables are dependent
Cell i
12930(48)/70 = 20.578.43 3.45
2130(22)/70 = 9.43 -8.43 7.54
31017(48)/70 = 11.66-1.66 .24
47 17(22)/70 = 5.34 1.66 .52
5 9 23(48)/70 = 15.77 -6.77 2.91
61423(22)/70 =7.23 6.77 6.34
Total 70 70 = 21.00
Rejection region: 5.99
= 21.00, p-value = 0. There is sufficient evidence to infer that the research findings are related to whether drug companies fund the research.
15.33 The two variables (degree and approach) are independent
The two variables are dependent
Cell i
15175(101)/195 = 38.8512.153.80
2875(31)/195 = 11.92-3.921.29
3575(36)/195 = 13.85-8.855.65
411 752(27)/195 = 10.38.62.04
5 24 58(101)/195 = 30.04-6.041.21
61458(31)/195 = 9.224.78 2.48
71258(36)/195 = 10.711.29.16
8858(27)/195 = 8.03-.030
926 62(101)/195 =32.11-6.111.16
10 9 62(31)/195 = 9.86-.86.07
11 19 62(36)/195 = 11.457.554.99
12862(27)/195 = 8.58-.58.04
Total195 195 = 20.89
Rejection region: 12.6
= 20.89, p-value = .0019. There is sufficient evidence to infer that there are differences in teaching approach among the four types of degree. The editor can design books and sales campaigns based on the distribution of degrees.
15.34The data are normally distributed
The data are not normally distributed
Expected Observed
Interval Probability Value Value
Z -1.5.0668 6.68 103.32 1.65
-1.5 < Z -0.5 .2417 24.17 18 -6.17 1.58
-0.5 < Z 0.5.3829 38.29 48 9.71 2.46
0.5 < Z 1.5 .2417 24.17 16 -8.17 2.76
Z > 1.5 .0668 6.68 81.32 0.26
Total 1100 100 = 8.71
Rejection region: 5.99
= 8.71, p-value = .0128. There is enough evidence to infer that the data are not normally distributed.
15.35The data are normally distributed
The data are not normally distributed
Expected Observed
Interval ProbabilityValue Value
Z -1.1587 7.946-1.94 0.47
-1 < Z 0.3413 17.07 279.93 5.78
0 < Z 1.3413 17.07 14-3.07 0.55
Z > 1.1587 7.94 3-4.94 3.07
Total 1 5050 = 9.87
Rejection region: 2.71
= 9.87, p-value = .0017. There is sufficient evidence to infer that the data are not normally distributed.
15.36Times are normally distributed
Times are not normally distributed.
= 16.62, p-value = .0002. There is sufficient evidence to infer that the amount of time at part-time jobs is not normally distributed.
15.37Costs are normally distributed
Costs are not normally distributed
= 506.76, p-value = 0. There is sufficient evidence to infer that drug costs are not normally distributed.
15.38Successful firms:
Productivity in successful firms is normally distributed
Productivity in successful firms is not normally distributed
=3.03, p-value = .2199. There is not enough evidence to infer that productivity in successful firms is not normally distributed.
Unsuccessful firms:
Productivity in unsuccessful firms is normally distributed
Productivity in unsuccessful firms is not normally distributed
= 1.13, p-value = .5670. There is not enough evidence to infer that productivity in unsuccessful firms is not normally distributed.
15.39 Reaction times are normally distributed
Reaction times re not normally distributed
Phone
= .2351, p-value = .8891. There is not enough evidence to infer that reaction times of those using the cell phone are not normally distributed.
Not on phone
= 3.1752, p-value = .2044. There is not enough evidence to infer that reaction times of those not using the cell phone are not normally distributed.
15.40Matched pairs differences of sales are normally distributed
Matched pairs differences ofsales are not normally distributed
= .055,p-value = .8140. There is not enough evidence to infer that matched pairs difference of sales is not normally distributed.
15.411/3, 1/3, 1/3
At least one is not equal to its specified value.
Cell i
1 1430(1/3) = 10 4 1.60
2 1030(1/3) = 10 0 0.00
3 630(1/3) = 10 -4 1.60
Total 30 30 = 3.20
Rejection region: 4.61
= 3.20, p-value = .2019. There is not enough evidence to infer that the game is unfair.
15.42.2, .2, .2, .2, .2
At least one is not equal to its specified value.
Cell i
1 87 362(.2) = 72.4 14.6 2.94
2 62 362(.2) = 72.4 -10.4 1.49
3 71 362(.2) = 72.4 -1.4 0.03
4 68 362(.2) = 72.4 -4.4 0.27
5 74 362(.2) = 72.4 1.6 0.04
Total 362 362 = 4.77
Rejection region: 9.49
= 4.77, p-value = .3119. There is not enough evidence to infer that absenteeism is higher on some days of the week.
15.43 The two variables (shift and day) are independent
The two variables are dependent
Cell i
1 52 181(87)/362 = 43.50 8.50 1.66
2 28 181(62)/362 = 31.00 -3.00 0.29
3 37 181(71)/362 = 35.50 -1.50 0.06
4 31 181(68)/362 = 34.00 -3.00 0.27
5 33 181(74)/362 = 37.00 -4.00 0.43
6 35 181(87)/362 = 43.50 -8.50 1.66
7 34 181(62)/362 = 31.00 3.00 0.29
8 34 181(71)/362 = 35.50 -1.50 0.06
9 37 181(68)/362 = 34.00 3.00 0.26
10 41 181(74)/362 = 37.00 4.00 0.43
Total 362 362 = 5.41
Rejection region: 7.78
= 5.41, p-value = .2465. There is not enough evidence to infer that there is a relationship between the days an employee is absent and the shift on which the employee works.
15.44 The two variables (satisfaction and relationship) are independent
The two variables are dependent
Cell i
121171(91)/447 = 34.81-13.81 5.48
225171(122)/447 = 46.67-21.6710.06
354171(114)/447 = 43.61 10.39 2.48
471171(120)/447 = 45.91 25.0913.72
539176(91)/447 = 35.83 3.17 0.28
649176(122)/447 = 48.04 0.96 0.02
750176(114)/447 = 44.89 5.11 0.58
838176(120)/447 = 47.25 -9.25 1.81
931100(91)/447 = 20.36 10.64 5 56
1048100(122)/447 = 27.29 20.7115.71
1110100(114)/447 = 25.50 -15.50 9.42
1211100(120)/447 = 26.85 -15.85 9.35
Total447 447 = 74.47
Rejection region: 12.6
= 74.47, p-value = 0. There is sufficient evidence to infer that the level of job satisfaction depends on boss/employee gender relationship.
15.45 The two variables (Country and stress) are independent
The two variables are dependent
= 20.3755, p-value = .0004. There is enough evidence to infer that Americans and Canadians differ in their sources of stress.
15.46 The two variables (method and quit) are independent
The two variables are dependent
= .5803, p-value = .9009. There is not enough evidence to infer that the four methods differ in their success rates.
15.47 The two variables (education and section) are independent
The two variables are dependent
= 86.6154, p-value = 0. There is sufficient evidence to infer that educational level affects the way adults read the newspaper.
15.48a The expected frequency is 1/49.
b 1/49, 1/49, . . . , 1/49
At least one is not equal to its specified value.
Number i
1 5 312(1/49) = 6.37 -1.38 0.29
2 6 312(1/49) = 6.37 -0.38 0.02
3 7 312(1/49) = 6.37 0.63 0.06
..
..
..
47 6 312(1/49) = 6.37 -0.37 0.02
48 10 312(1/49) = 6.37 3.63 2.07
49 6 312(1/49) = 6.37 -0.37 0.02
Total 312 312 = 38.22
= 38.22, p-value = .8427. There is not enough evidence to infer that the numbers were not generated randomly.
15.49 The two variables (income and RRSP) are independent
The two variables are dependent
= 15.8838, p-value = .0032. There is enough evidence to infer that there are differences in RRSP positions among the five income brackets.
15.50 Binomial probabilities with n = 5 and p = .5: P(X = 0) = .0313, P(X = 1) = .1563, P(X = 2) = .3125, P(X = 3) = .3125, P(X = 4) = .1563, P(X = 5) = .0313
.0313,.1563, .3125, .3125, .1563, .0313
At least one is not equal to its specified value.
Cell i
0 8 200(.0313) = 6.26 1.74 0.48
1 35 200(.1563) = 31.26 3.74 0.45
2 57 200(.3125) = 62.50 -5.50 0.48
3 69 200(.3125) = 62.50 6.50 0.68
4 28 200(.1563) = 31.26 -3.26 0.34
5 3 200(.0313) = 6.26 -3.26 1.70
Total 200 200 = 4.13
Rejection region: 11.1
= 4.13, p-value = .5310. There is not enough evidence to infer that at the number of boys in families with 5 children is not a binomial random variable with p =.5.
15.51 The two variables (cold and group) are independent
The two variables are dependent
= 4.139, p-value = .2468. There is not enough evidence to infer there are differences between the four groups.
15.52 The two variables (faculty and retire) are independent
The two variables are dependent
= 9.732, p-value = .0452. There is enough evidence to infer that whether a professor wishes to retire is related to the faculty.
15.53 The two variables (tree choice and age category) are independent
The two variables are dependent
= 38.41, p-value = 0. There is enough evidence to infer that there are differences in the choice of Christmas tree between the three age categories.
15.54 The two variables (network and ask) are independent
The two variables are dependent
= 4.573, p-value = .1016. There is not enough evidence to conclude that there are differences in responses between the three network news shows.
15.55 The two variables (newspaper and subscribe) are independent
The two variables are dependent
= 12.8731, p-value = .0016. There is enough evidence to infer that the response to subscribing to the new newspaper differs between the readers of the current newspapers.
15.56 a The two variables (education and group) are independent
The two variables are dependent
= 26.7059, p-value = 0. There is enough evidence to infer that there are differences in educational attainment between those who belong and those who do not belong to the health conscious group.
b The two variables (education and buy Special X) are independent
The two variables are dependent
= 2.9416, p-value = .4007. There is not enough evidence to infer that there is a relationship between the four education groups and whether a person buys Special X.
15.57 The two variables (income category and show) are independent
The two variables are dependent
= 23.96, p-value = .0206. There is enough evidence to conclude that what people watchedon Sunday April 1, 2007 at 9:00 P.M. was related to income.
15.58 a The two variables (gender and vote) are independent
The two variables are dependent
= .6483, p-value = .4207. There is not enough evidence to infer that voting and gender are related.
b The two variables (education and vote) are independent
The two variables are dependent
= 7.7214, p-value = .0521. There is not enough evidence to infer that voting and educational level are related.
c The two variables (income category and vote) are independent
The two variables are dependent
= 23.108, p-value = 0. There is enough evidence to infer that voting and income are related.
15.59 The two variables are (type of work and segment) independent
The two variables are dependent
= 23.0946, p-value = .0001. There is enough evidence to infer that there are differences in employment between the three market segments.
15.60 The two variables (value and segment) are independent
The two variables are dependent
= 4.5122, p-value = .3411. There is not enough evidence to infer that there are differences in the definition of value between the three market segments.
15.61 The two variables (breakfast and group) are independent
The two variables are dependent
= 206.4908, p-value = 0. There is enough evidence to infer that there are differences in frequency of healthy breakfasts between the three four segments.
Case 15.1 The two variables are independent
The two variables are dependent
= 12.6165, p-value = .0055. There is enough evidence to infer that there are differences between the four professional sports in terms of whether early-game leaders win the game.
= 10.5184, p-value = .0146. There is enough evidence to infer that there are differences among the four professional sports in terms of whether late-game leaders win the game.
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