a) Acme Toy Company prints baseball cards. The company claims that 30% of the cards are Rookies, 60% Veterans but not All-Stars, and 10% are Veteran All-Stars. Suppose a random sample of 100 cards has 50 Rookies, 45 Veterans, and 5 Veterans All-Stars. Table 1: Veterans Veteran All-Star Rookies 50 Observed 45 Expected 10 30 60 i) Set-up a hypothesis test to test if this information is consistent with the Acme's company claim? Use a 0.05 level of significance. Hint: Use chisquare goodness of fit test. ii) Suppose the random sample of 100 cards is said to have a standard deviation of 10.58 %, find a 90 % confidence interval for the population standard deviation.
a) Acme Toy Company prints baseball cards. The company claims that 30% of the cards are Rookies, 60% Veterans but not All-Stars, and 10% are Veteran All-Stars. Suppose a random sample of 100 cards has 50 Rookies, 45 Veterans, and 5 Veterans All-Stars. Table 1: Veterans Veteran All-Star Rookies 50 Observed 45 Expected 10 30 60 i) Set-up a hypothesis test to test if this information is consistent with the Acme's company claim? Use a 0.05 level of significance. Hint: Use chisquare goodness of fit test. ii) Suppose the random sample of 100 cards is said to have a standard deviation of 10.58 %, find a 90 % confidence interval for the population standard deviation.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Kindly assist
![CHI-SQUARED DISTRIBUTION: One sided critical values, i.e. the value of
) such that P = Pr[xår > xa"1, where df is the degrees of freedom, for P> 0.5
continued. CHI-SQUARED DISTRIBUTION: One sided critical values, i.e.
2(P)1
the value of x such that P = Prlxåy > xay"], where df is the degrees of freedom,
2(P)
%3D
Xdf
for P< 0.5
Probability Level P
Probability Level P
0.025
df
0.9995
0.999
0.9975
0.995
0.99
0.975
0.95
0.9
0.8
0.6
df
0.4
0.2
1.642
0.005
7.879
0.1
0.05
0.0025
9.140
0.01
0.001
0.0005
1
0.000
0.000
0.000
0.000
0.000
0.001
0.004
0.016
0.064
0.275
0.708
5.024
7.378
2.706
3.841
6.635
10.827
12.115
0.005
0.045
0.001
0.002
0.010
0.020
0.051
0.103
0.211
0.446
1.022
1.833
3.219
4.605
5.991
9.210
10.597
11.983
13.815
15.201
3.
0.015
0.024
0.072
0.115
0.216
0.352
0.584
1.005
1.869
4.642
5.989
3.
2.946
6.251
7.815
9.348
11.345
12.838
14.320
16.266
17.731
4.
0.064
0.091
0.145
0.207
0.297
0.484
0.711
1.064
1.649
2.753
4.
4.045
779
9.488
11.143
13.277
14.860
18.466
16.424
19.998
0.158
0.210
0.307
0.412
0.554
0.831
1.145
1.610
2.343
3.656
5.132
7.289
9.236
11.070
12.832
15.086
16.750
18.385
20.515
22.106
24.102
26.018
6.
0.299
0.381
0.527
0.676
0.872
4.570
5.493
1.237
1.635
2.204
3.070
6.
6.211
8.558
10.645
12.592
14.449
16.812
18.548
20.249
22.457
7.
0.485
0.599
0.794
0.989
1.239
1.690
2.167
2.833
3.822
7.283
9.803
12.017
14.067
16.013
18.475
24.321
26.124
20.278
22.040
8.
0.710
0.972
0.857
1.104
1.344
1.647
2.180
8.351
2.733
3.325
3.940
3.490
4.594
6.423
11.030
13.362
15.507
17.535
20.090
21.955
23.774
27.867
1.152
1.450
1.735
2.088
2.700
4.168
5.380
7.357
9.
9.414
12.242
14.684
16.919
19.023
21.666
23.589
25.463
27.877
29.667
10
1.265
1.479
1.827
2.156
2.558
3.247
4.865
6.179
8.295
10
10.473
13.442
15.987
18.307
20.483
23.209
25.188
27.112
29.588
31.419
11
1.587
1.834
2.232
2.603
3.053
3.816
4.575
5.226
5.578
6.989
9.237
11
11.530
14.631
17.275
19.675
21.920
24.725
26.757
28.729
31.264
33.138
12
1.935
2.214
2.661
3.074
3.571
4.404
6.304
7.807
10.182
12
12.584
15.812
18.549
21.026
23.337
26.217
28.300
30.318
32.909
34.821
13
2.305
3.112
3.582
2.617
3.565
5.009
13
13.636
16.985
18.151
4.107
5.892
7.041
8.634
11.129
19.812
22.362
24.736
27.688
29.819
31.883
34.527
36.477
14
2.697
3.041
4.075
4.660
5.629
7.790
14
14.685
21.064
23.685
29.141
6.571
7.261
9.467
10.307
26.119
31.319
33.426
36.124
12.078
13.030
38.109
15
3.107
3.483
4.070
4.601
5.229
6.262
8.547
15
15.733
19.311
22.307
24.996
27.488
30.578
32.801
34.949
37.698
39.717
16
3.536
3.942
4.573
5.142
5.812
6.908
7.962
16
16.780
20.465
23.542
26.296
28.845
39.252
40.791
9.312
11.152
13.983
32.000
34.267
36.456
41.308
17
3.980
4.416
5.092
5.697
6.408
7.564
8.672
10.085
12.002
14.937
17
17.824
21.615
24.769
27.587
30.191
33.409
35.718
37.946
42.881
18
4.439
4.905
5.623
6.265
7.015
8.231
9.390
10.865
12.857
15.893
18
18.868
22.760
25.989
28.869
31.526
34.805
37.156
39.422
42.312
44.434
19
4.913
5.407
6.167
6.844
7.633
8.907
10.117
11.651
13.716
16.850
19
19.910
23.900
27.204
30.144
32.852
36.191
38.582
40.885
43.819
45.974
20
5.398
5.895
5.921
6.723
7.434
20
20.951
25.038
28.412
31.410
34.170
37.566
39.997
42.336
43.775
8.260
9.591
10.851
12.443
14.578
17.809
45.314
47.498
21
6.447
7.289
8.034
8.897
10.283
11.591
13.240
15.445
18.768
21
21.992
26.171
29.615
32.671
35.479
38.932
41.401
46.796
49.010
22
6.404
6.983
7.865
8.643
9.542
10.982
12.338
14.041
16.314
19.729
22
23.031
27.301
30.813
33.924
36.781
40.289
42.796
45.204
48.268
50.510
24.069
25.106
23
6.924
7.529
8.450
9.260
10.196
11.689
13.091
14.848
17.187
20.690
23
28.429
32.007
35.172
38.076
41.638
44.181
46.623
49.728
51.999
24
7.453
8.085
9.044
9.886
10.856
24
29.553
33.196
36.415
39.364
42.980
45.558
48.034
49.435
50.829
12.401
13.848
15.659
18.062
21.652
51.179
53.478
30.675
31.795
25
7.991
8.649
9.646
10.520
11.524
13.120
14.611
16.473
18.940
22.616
25
26.143
34.382
37.652
40.646
44.314
46.928
52.619
54.948
26
8.537
9.222
26
27.179
35.563
12.198
12.878
10.256
11.160
13.844
17.292
38.885
41.923
45.642
48.290
54.051
56.407
15.379
16.151
19.820
23.579
24.544
25.509
27
9.093
9.803
10.873
11.808
14.573
18.114
20.703
27
28.214
32.912
36.741
40.113
43.195
46.963
49.645
52.215
55.475
57.856
28
9.656
10.391
28
29.249
34.027
37.916
39.087
11.497
12.461
13.565
15.308
16.928
18.939
21.588
41.337
44.461
48.278
50.994
53.594
56.892
59.299
29
10.227
10.986
29
30.283
35.139
42.557
45.722
49.588
50.892
12.128
13.121
14.256
16.047
17.708
19.768
22.475
26.475
52.335
54.966
58.301
60.734
30
10.804
11.588
12.765
13.787
14.953
16.791
18.493
20.599
23.364
27.442
30
31.316
36.250
40.256
43.773
46.979
53.672
56.332
59.702
62.160
31
11.388
12.196
13.407
14.458
15.655
17.539
19.281
21.434
24.255
31
32.349
37.359
41.422
44.985
48.232
52.191
55.002
57.692
61.098
63.581
28.409
29.376
32
33.381
42.585
43.745
32
11.980
12.810
14.055
38.466
46.194
49.480
53.486
56.328
59.046
62.487
64.993
15.134
15.815
16.362
18.291
19.047
20.072
22.271
25.148
33
12.576
13.431
14.709
17.073
20.867
23.110
26.042
30.344
33
34.413
39.572
47.400
50.725
54.775
57.648
60.395
63.869
66.401
34
34
35.444
40.676
44.903
48.602
51.966
67.804
69.197
13.180
14.057
15.368
16.501
17.789
19.806
21.664
23.952
26.938
31.313
56.061
58.964
61.738
65.247
35
13.788
14.688
16.032
17.192
18.509
20.569
22.465
24.797
27.836
32.282
35
36.475
41.778
46.059
49.802
53.203
57.342
60.275
63.076
66.619
36
14.401
15.324
16.700
17.887
19.233
21.336
23.269
25.643
28.735
33.252
36
37.505
42.879
47.212
50.998
54.437
58.619
61.581
64.410
67.985
70.588
37
37
38.535
43.978
48.363
52.192
55.668
59.893
62.883
65.738
69.348
70.704
72.055
73.403
15.021
15.965
17.373
18.586
19.960
22.106
24.075
26.492
29.635
34.222
71.971
38
39.564
45.076
49.513
53.384
54.572
56.895
61.162
64.181
67.063
15.644
16.272
38
16.611
18.050
19.289
20.691
22.878
73.350
24.884
25.695
27.343
28.196
30.537
35.192
39
17.261
18.732
19.996
21.426
23.654
39
40.593
46.173
50.660
58.120
62.428
65.475
68.383
74.724
31.441
36.163
40
16.906
17.917
19.417
20.707
22.164
24.433
26.509
29.051
32.345
37.134
40
41.622
47.269
51.805
55.758
59.342
63.691
66.766
69.699
76.096
45
20.136
21.251
22.899
24.311
25.901
28.366
30.612
33.350
36.884
41.995
45
46.761
52.729
57.505
61.656
65.410
69.957
73.166
76.223
80.078
82.873
50
23.461
24.674
26.464
27.991
29.707
32.357
34.764
37.689
41.449
50
51.892
58.164
63.167
67.505
71.420
76.154
79.490
82.664
86.660
89.560
46.864
60
62.135
68.972
74.397
79.082
83.298
95.023 100.425 104.215
60
30.339
31.738
33.791
35.534
37.485
40.482
43.188
46.459
50.641
56.620
88.379
91.952
95.344
99.608
102.697
70
72.358
79.715
85.527
96.578
70
90.531
107.808 112.317
115.577
37.467
44.792
39.036
41.332
43.275
45.442
48.758
51.739
55.329
59.898
66.396
80
46.520
49.043
51.172
53.540
57.153
60.391
64.278
69.207
80
82.566
90.405
101.879
106.629 112.329 116.321
120.102 124.839
128.264
76.188
92.761
100 102.946 111.667
110 113.121 122.250
120 123.289
140 143.604
160 163.898
180 184.173
200 204.434 216.609
90
52.277
54.156
56.892
59.196
61.754
65.647
69. 126
73.291
78.558
85.993
90
101.054 107.565 113.145
118.136 124.116 128.299
132.255
137.208
140.780
100
59.895
61.918
64.857
67.328
70.065
74.222
77.929
82.358
87.945
95.808
118.498
124.342
129.561 135.807 140.17O
144.292 149.449
153.164
129.385
135.480
140.916 147A14 151.948
152.211 158.950
110
67.631
69.790
72.922
75.550
78.458
82.867
86.792
91.471
97.362
105.632
156.230 161.582
165.436
132.806 140.233
146.567
163.648
168.081
173.618
177.601
191.565 197.450 201.680
120
75.465
77.756
81.073
83.852
86.923
100.655 104.034
91.573
95.705 100.624
106.806 115. 465
125.758
153.854
174.828
140
91.389
93.925
97,591
161.827
168.613
174.648
181.841
186.847
109.137
113.659
119.029
135.149
183.311
190.516
196.915 204.530 209.824 214.808 221.020 225.477
107.599 110.359
180 124.032 127.011
200 140.659 143.842
160
114.350
117.679 121.346
126.870
131.756 137.546
144.741 149.969 156.153 163.868 174.580
144.783 154.856
195.743
204.704 212.304 219.044
227.056 232.620
237.855 244.372 249.049
131.305
134.884 138.821
148.426
152.241 156.432
162.728
168.279 174.835
183.003 194.319
226.021
233.994
241.058 249.445 255.264
260.735 267.539 272.422
8
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Transcribed Image Text:CHI-SQUARED DISTRIBUTION: One sided critical values, i.e. the value of
) such that P = Pr[xår > xa"1, where df is the degrees of freedom, for P> 0.5
continued. CHI-SQUARED DISTRIBUTION: One sided critical values, i.e.
2(P)1
the value of x such that P = Prlxåy > xay"], where df is the degrees of freedom,
2(P)
%3D
Xdf
for P< 0.5
Probability Level P
Probability Level P
0.025
df
0.9995
0.999
0.9975
0.995
0.99
0.975
0.95
0.9
0.8
0.6
df
0.4
0.2
1.642
0.005
7.879
0.1
0.05
0.0025
9.140
0.01
0.001
0.0005
1
0.000
0.000
0.000
0.000
0.000
0.001
0.004
0.016
0.064
0.275
0.708
5.024
7.378
2.706
3.841
6.635
10.827
12.115
0.005
0.045
0.001
0.002
0.010
0.020
0.051
0.103
0.211
0.446
1.022
1.833
3.219
4.605
5.991
9.210
10.597
11.983
13.815
15.201
3.
0.015
0.024
0.072
0.115
0.216
0.352
0.584
1.005
1.869
4.642
5.989
3.
2.946
6.251
7.815
9.348
11.345
12.838
14.320
16.266
17.731
4.
0.064
0.091
0.145
0.207
0.297
0.484
0.711
1.064
1.649
2.753
4.
4.045
779
9.488
11.143
13.277
14.860
18.466
16.424
19.998
0.158
0.210
0.307
0.412
0.554
0.831
1.145
1.610
2.343
3.656
5.132
7.289
9.236
11.070
12.832
15.086
16.750
18.385
20.515
22.106
24.102
26.018
6.
0.299
0.381
0.527
0.676
0.872
4.570
5.493
1.237
1.635
2.204
3.070
6.
6.211
8.558
10.645
12.592
14.449
16.812
18.548
20.249
22.457
7.
0.485
0.599
0.794
0.989
1.239
1.690
2.167
2.833
3.822
7.283
9.803
12.017
14.067
16.013
18.475
24.321
26.124
20.278
22.040
8.
0.710
0.972
0.857
1.104
1.344
1.647
2.180
8.351
2.733
3.325
3.940
3.490
4.594
6.423
11.030
13.362
15.507
17.535
20.090
21.955
23.774
27.867
1.152
1.450
1.735
2.088
2.700
4.168
5.380
7.357
9.
9.414
12.242
14.684
16.919
19.023
21.666
23.589
25.463
27.877
29.667
10
1.265
1.479
1.827
2.156
2.558
3.247
4.865
6.179
8.295
10
10.473
13.442
15.987
18.307
20.483
23.209
25.188
27.112
29.588
31.419
11
1.587
1.834
2.232
2.603
3.053
3.816
4.575
5.226
5.578
6.989
9.237
11
11.530
14.631
17.275
19.675
21.920
24.725
26.757
28.729
31.264
33.138
12
1.935
2.214
2.661
3.074
3.571
4.404
6.304
7.807
10.182
12
12.584
15.812
18.549
21.026
23.337
26.217
28.300
30.318
32.909
34.821
13
2.305
3.112
3.582
2.617
3.565
5.009
13
13.636
16.985
18.151
4.107
5.892
7.041
8.634
11.129
19.812
22.362
24.736
27.688
29.819
31.883
34.527
36.477
14
2.697
3.041
4.075
4.660
5.629
7.790
14
14.685
21.064
23.685
29.141
6.571
7.261
9.467
10.307
26.119
31.319
33.426
36.124
12.078
13.030
38.109
15
3.107
3.483
4.070
4.601
5.229
6.262
8.547
15
15.733
19.311
22.307
24.996
27.488
30.578
32.801
34.949
37.698
39.717
16
3.536
3.942
4.573
5.142
5.812
6.908
7.962
16
16.780
20.465
23.542
26.296
28.845
39.252
40.791
9.312
11.152
13.983
32.000
34.267
36.456
41.308
17
3.980
4.416
5.092
5.697
6.408
7.564
8.672
10.085
12.002
14.937
17
17.824
21.615
24.769
27.587
30.191
33.409
35.718
37.946
42.881
18
4.439
4.905
5.623
6.265
7.015
8.231
9.390
10.865
12.857
15.893
18
18.868
22.760
25.989
28.869
31.526
34.805
37.156
39.422
42.312
44.434
19
4.913
5.407
6.167
6.844
7.633
8.907
10.117
11.651
13.716
16.850
19
19.910
23.900
27.204
30.144
32.852
36.191
38.582
40.885
43.819
45.974
20
5.398
5.895
5.921
6.723
7.434
20
20.951
25.038
28.412
31.410
34.170
37.566
39.997
42.336
43.775
8.260
9.591
10.851
12.443
14.578
17.809
45.314
47.498
21
6.447
7.289
8.034
8.897
10.283
11.591
13.240
15.445
18.768
21
21.992
26.171
29.615
32.671
35.479
38.932
41.401
46.796
49.010
22
6.404
6.983
7.865
8.643
9.542
10.982
12.338
14.041
16.314
19.729
22
23.031
27.301
30.813
33.924
36.781
40.289
42.796
45.204
48.268
50.510
24.069
25.106
23
6.924
7.529
8.450
9.260
10.196
11.689
13.091
14.848
17.187
20.690
23
28.429
32.007
35.172
38.076
41.638
44.181
46.623
49.728
51.999
24
7.453
8.085
9.044
9.886
10.856
24
29.553
33.196
36.415
39.364
42.980
45.558
48.034
49.435
50.829
12.401
13.848
15.659
18.062
21.652
51.179
53.478
30.675
31.795
25
7.991
8.649
9.646
10.520
11.524
13.120
14.611
16.473
18.940
22.616
25
26.143
34.382
37.652
40.646
44.314
46.928
52.619
54.948
26
8.537
9.222
26
27.179
35.563
12.198
12.878
10.256
11.160
13.844
17.292
38.885
41.923
45.642
48.290
54.051
56.407
15.379
16.151
19.820
23.579
24.544
25.509
27
9.093
9.803
10.873
11.808
14.573
18.114
20.703
27
28.214
32.912
36.741
40.113
43.195
46.963
49.645
52.215
55.475
57.856
28
9.656
10.391
28
29.249
34.027
37.916
39.087
11.497
12.461
13.565
15.308
16.928
18.939
21.588
41.337
44.461
48.278
50.994
53.594
56.892
59.299
29
10.227
10.986
29
30.283
35.139
42.557
45.722
49.588
50.892
12.128
13.121
14.256
16.047
17.708
19.768
22.475
26.475
52.335
54.966
58.301
60.734
30
10.804
11.588
12.765
13.787
14.953
16.791
18.493
20.599
23.364
27.442
30
31.316
36.250
40.256
43.773
46.979
53.672
56.332
59.702
62.160
31
11.388
12.196
13.407
14.458
15.655
17.539
19.281
21.434
24.255
31
32.349
37.359
41.422
44.985
48.232
52.191
55.002
57.692
61.098
63.581
28.409
29.376
32
33.381
42.585
43.745
32
11.980
12.810
14.055
38.466
46.194
49.480
53.486
56.328
59.046
62.487
64.993
15.134
15.815
16.362
18.291
19.047
20.072
22.271
25.148
33
12.576
13.431
14.709
17.073
20.867
23.110
26.042
30.344
33
34.413
39.572
47.400
50.725
54.775
57.648
60.395
63.869
66.401
34
34
35.444
40.676
44.903
48.602
51.966
67.804
69.197
13.180
14.057
15.368
16.501
17.789
19.806
21.664
23.952
26.938
31.313
56.061
58.964
61.738
65.247
35
13.788
14.688
16.032
17.192
18.509
20.569
22.465
24.797
27.836
32.282
35
36.475
41.778
46.059
49.802
53.203
57.342
60.275
63.076
66.619
36
14.401
15.324
16.700
17.887
19.233
21.336
23.269
25.643
28.735
33.252
36
37.505
42.879
47.212
50.998
54.437
58.619
61.581
64.410
67.985
70.588
37
37
38.535
43.978
48.363
52.192
55.668
59.893
62.883
65.738
69.348
70.704
72.055
73.403
15.021
15.965
17.373
18.586
19.960
22.106
24.075
26.492
29.635
34.222
71.971
38
39.564
45.076
49.513
53.384
54.572
56.895
61.162
64.181
67.063
15.644
16.272
38
16.611
18.050
19.289
20.691
22.878
73.350
24.884
25.695
27.343
28.196
30.537
35.192
39
17.261
18.732
19.996
21.426
23.654
39
40.593
46.173
50.660
58.120
62.428
65.475
68.383
74.724
31.441
36.163
40
16.906
17.917
19.417
20.707
22.164
24.433
26.509
29.051
32.345
37.134
40
41.622
47.269
51.805
55.758
59.342
63.691
66.766
69.699
76.096
45
20.136
21.251
22.899
24.311
25.901
28.366
30.612
33.350
36.884
41.995
45
46.761
52.729
57.505
61.656
65.410
69.957
73.166
76.223
80.078
82.873
50
23.461
24.674
26.464
27.991
29.707
32.357
34.764
37.689
41.449
50
51.892
58.164
63.167
67.505
71.420
76.154
79.490
82.664
86.660
89.560
46.864
60
62.135
68.972
74.397
79.082
83.298
95.023 100.425 104.215
60
30.339
31.738
33.791
35.534
37.485
40.482
43.188
46.459
50.641
56.620
88.379
91.952
95.344
99.608
102.697
70
72.358
79.715
85.527
96.578
70
90.531
107.808 112.317
115.577
37.467
44.792
39.036
41.332
43.275
45.442
48.758
51.739
55.329
59.898
66.396
80
46.520
49.043
51.172
53.540
57.153
60.391
64.278
69.207
80
82.566
90.405
101.879
106.629 112.329 116.321
120.102 124.839
128.264
76.188
92.761
100 102.946 111.667
110 113.121 122.250
120 123.289
140 143.604
160 163.898
180 184.173
200 204.434 216.609
90
52.277
54.156
56.892
59.196
61.754
65.647
69. 126
73.291
78.558
85.993
90
101.054 107.565 113.145
118.136 124.116 128.299
132.255
137.208
140.780
100
59.895
61.918
64.857
67.328
70.065
74.222
77.929
82.358
87.945
95.808
118.498
124.342
129.561 135.807 140.17O
144.292 149.449
153.164
129.385
135.480
140.916 147A14 151.948
152.211 158.950
110
67.631
69.790
72.922
75.550
78.458
82.867
86.792
91.471
97.362
105.632
156.230 161.582
165.436
132.806 140.233
146.567
163.648
168.081
173.618
177.601
191.565 197.450 201.680
120
75.465
77.756
81.073
83.852
86.923
100.655 104.034
91.573
95.705 100.624
106.806 115. 465
125.758
153.854
174.828
140
91.389
93.925
97,591
161.827
168.613
174.648
181.841
186.847
109.137
113.659
119.029
135.149
183.311
190.516
196.915 204.530 209.824 214.808 221.020 225.477
107.599 110.359
180 124.032 127.011
200 140.659 143.842
160
114.350
117.679 121.346
126.870
131.756 137.546
144.741 149.969 156.153 163.868 174.580
144.783 154.856
195.743
204.704 212.304 219.044
227.056 232.620
237.855 244.372 249.049
131.305
134.884 138.821
148.426
152.241 156.432
162.728
168.279 174.835
183.003 194.319
226.021
233.994
241.058 249.445 255.264
260.735 267.539 272.422
8
7
Transcribed Image Text:Question 5
Inferencial statistics
a) Acme Toy Company prints baseball cards. The company claims that 30% of the cards are Rookies,
60% Veterans but not All-Stars, and 10% are Veteran All-Stars.
Suppose a random sample of 100 cards has 50 Rookies, 45 Veterans, and 5 Veterans All-Stars.
Table 1:
Veterans
45
Veteran All-Star
Rookies
50
Observed
Expected
30
60
10
i) Set-up a hypothesis test to test if this information is consistent with the Acme's company claim? Use a
0.05 level of significance.
Hint: Use chisquare goodness of fit test.
ii) Suppose the random sample of 100 cards is said to have a standard deviation of 10.58 %, find a 90 %
confidence interval for the population standard deviation.
b) An analysis of the tries, penalty goals and dropped goals scored by South Africa in rugby tests against
the British Isles, New Zealand, Australia and France gave the following contingency table:
Table 2:
Tries Penalties Drops
70
British Isles
New Zealand
Australia
France
31
6.
44
38
11
79
31
32
7
43
3
The number of penalities scored against New Zealand and France seems unexpectedly high, and this
leads you to want to test the hypothesis that the mode of scoring is dependent on the opponents. At
5% level of significance, can you carry out a test for association?
Hint: Use chisquare test for independence/association.
NB: Make use of the chi-squared distribution table on "Appendix".
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