Last year labour union agents listed five categories and asked a number of employees to mark the one most important to her/him. The categories and corresponding percentages of favourable responses are listed in table 1. A new survey has been performed, and the agents need to determine whether the current distribution of responses deviates from the previous year. The results of this new survey are listed in table 2.Establish two working hypotheses, namely null-hypothesis, , and alternative hypothesis, .Use a Chi-square distribution to test the goodness-of-fit between the sample statisticsAccount for the degrees of freedomUsing the degrees of freedom estimate a critical value for testing the sample statistics at a 99% confidence level (1% level of significance)Conclude the test and interpret the conclusionTable 1. Categories in a union surveyCategoryPercentage of Favourable ResponsesVacation time4%Salary65%Safety regulations13%Health and retirement benefits12%Overtime policy and pay6%Table 2. Survey responses new surveyCategoryObserved Favourable ResponsesVacation time30Salary290Safety regulations70Health and retirement benefits70Overtime policy and pay40Values of the Chi-square test, df = degrees of freedom(image) Level of Significance adf0.2000.1000.0750.0500.0250.0100.0050.0010.000511.6422.7063.1703.8415.0246.6357.87910.82812.1163.2194.6055.1815.9917.3789.21010.59713.81615.20234.6426.2516.9057.8159.34811.34512.83816.26617.73145.9897.7798.4969.48811.14313.27714.86018.46719.99857.2899.23610.00811.07012.83315.08616.75020.51622.10668.55810.64511.46612.59214.44916.81218.54822.45824.10479.80312.01712.88314.06716.01318.47520.27824.32226.0198.11.03013.36214.27015.50717.53520.09021.95526.12527.8699.12.24214.68415.63116.91919.02321.66623.58927.87829.6671013.44215.98716.97118.30720.48323.20925.18829.58931.4211114.63117.27518.29419.67521.92024.72526.75731.26533.1381215.81218.54919.60221.02623.33726.21728.30032.91034.8221316.98519.81220.89722.36224.73627.68829.82034.52936.4791418.15121.06422.18023.68526.11929.14131.31936.12438.1111519.31122.30723.45224.99627.48830.57832.80137.69839.7201620.46523.54224.71626.29628.84532.00034.26739.25341.3091721.61524.76925.97027.58730.19133.40935.71940.79142.8811822.76025.98927.21828.86931.52634.80537.15742.31444.4351923.90027.20428.45830.14432.85236.19138.58243.82145.9742025.03828.41229.69231.41034.17037.56639.99745.31547.5012126.17129.61530.92032.67135.47938.93241.40146.79849.0132227.30130.81332.14233.92436.78140.28942.79648.26950.5122328.42932.00733.36035.17238.07641.63944.18249.72952.0022429.55333.19634.57236.41539.36442.98045.55951.18053.4802530.67534.38235.78037.65340.64644.31446.92852.62054.9502631.79535.56336.98438.88541.92345.64248.29054.05356.4092732.91236.74138.18440.11343.19546.96349.64555.47757.8602834.02737.91639.38041.33744.46148.27850.99456.89459.30240.57358.30252.33653.6722935.13939.08742.55745.72249.58860.7383036.25040.25641.76243.77346.97950.89259.70462.1644047.26951.80553.50155.75959.34263.69166.76673.40376.0975058.16463.16765.03067.50571.42076.15479.49086.66289.5646068.97274.39776.41179.08283.29888.38091.95299.609102.6987079.71585.52787.68090.53195.023100.425104.215112.319115.5828090.40596.57898.861101.880106.629112.329116.321124.842128.26790101.054107.565109.969113.145118.136124.117128.300137.211140.78900111.667118.498121.017124.342129.561135.807140.170149.452153.174

Use the given data to form excel table consisting of observed frequency, expected probability,…

Last year labour union agents listed five categories and asked a number of employees to mark the one most important to her/him. The categories and corresponding percentages of favourable responses are listed in table 1. A new survey has been performed, and the agents need to determine whether the current distribution of responses deviates from the previous year. The results of this new survey are listed in table 2. Establish two working hypotheses, namely null-hypothesis, , and alternative hypothesis, . Use a Chi-square distribution to test the goodness-of-fit between the sample statistics Account for the degrees of freedom Using the degrees of freedom estimate a critical value for testing the sample statistics at a 99% confidence level (1% level of significance) Conclude the test and interpret the conclusion Table 1. Categories in a union survey Category Percentage of Favourable Responses Vacation time 4% Salary 65% Safety regulations 13% Health and retirement benefits 12% Overtime policy and pay 6% Table 2. Survey responses new survey Category Observed Favourable Responses Vacation time 30 Salary 290 Safety regulations 70 Health and retirement benefits 70 Overtime policy and pay 40 Values of the Chi-square test, df = degrees of freedom

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Last year labour union agents listed five categories and asked a number of employees to mark the one most important to her/him. The categories and corresponding percentages of favourable responses are listed in table 1. A new survey has been performed, and the agents need to determine whether the current distribution of responses deviates from the previous year. The results of this new survey are listed in table 2.

Establish two working hypotheses, namely null-hypothesis, , and alternative hypothesis, .
Use a Chi-square distribution to test the goodness-of-fit between the sample statistics
Account for the degrees of freedom
Using the degrees of freedom estimate a critical value for testing the sample statistics at a 99% confidence level (1% level of significance)
Conclude the test and interpret the conclusion

Table 1. Categories in a union survey

Category	Percentage of Favourable Responses
Vacation time	4%
Salary	65%
Safety regulations	13%
Health and retirement benefits	12%
Overtime policy and pay	6%

Table 2. Survey responses new survey

Category	Observed Favourable Responses
Vacation time	30
Salary	290
Safety regulations	70
Health and retirement benefits	70
Overtime policy and pay	40

Values of the Chi-square test, df = degrees of freedom

(image)

Level of Significance a
df
0.200
0.100
0.075
0.050
0.025
0.010
0.005
0.001
0.0005
1
1.642
2.706
3.170
3.841
5.024
6.635
7.879
10.828
12.116
3.219
4.605
5.181
5.991
7.378
9.210
10.597
13.816
15.202
3
4.642
6.251
6.905
7.815
9.348
11.345
12.838
16.266
17.731
4
5.989
7.779
8.496
9.488
11.143
13.277
14.860
18.467
19.998
5
7.289
9.236
10.008
11.070
12.833
15.086
16.750
20.516
22.106
6
8.558
10.645
11.466
12.592
14.449
16.812
18.548
22.458
24.104
7
9.803
12.017
12.883
14.067
16.013
18.475
20.278
24.322
26.019
8.
11.030
13.362
14.270
15.507
17.535
20.090
21.955
26.125
27.869
9.
12.242
14.684
15.631
16.919
19.023
21.666
23.589
27.878
29.667
10
13.442
15.987
16.971
18.307
20.483
23.209
25.188
29.589
31.421
11
14.631
17.275
18.294
19.675
21.920
24.725
26.757
31.265
33.138
12
15.812
18.549
19.602
21.026
23.337
26.217
28.300
32.910
34.822
13
16.985
19.812
20.897
22.362
24.736
27.688
29.820
34.529
36.479
14
18.151
21.064
22.180
23.685
26.119
29.141
31.319
36.124
38.111
15
19.311
22.307
23.452
24.996
27.488
30.578
32.801
37.698
39.720
16
20.465
23.542
24.716
26.296
28.845
32.000
34.267
39.253
41.309
17
21.615
24.769
25.970
27.587
30.191
33.409
35.719
40.791
42.881
18
22.760
25.989
27.218
28.869
31.526
34.805
37.157
42.314
44.435
19
23.900
27.204
28.458
30.144
32.852
36.191
38.582
43.821
45.974
20
25.038
28.412
29.692
31.410
34.170
37.566
39.997
45.315
47.501
21
26.171
29.615
30.920
32.671
35.479
38.932
41.401
46.798
49.013
22
27.301
30.813
32.142
33.924
36.781
40.289
42.796
48.269
50.512
23
28.429
32.007
33.360
35.172
38.076
41.639
44.182
49.729
52.002
24
29.553
33.196
34.572
36.415
39.364
42.980
45.559
51.180
53.480
25
30.675
34.382
35.780
37.653
40.646
44.314
46.928
52.620
54.950
26
31.795
35.563
36.984
38.885
41.923
45.642
48.290
54.053
56.409
27
32.912
36.741
38.184
40.113
43.195
46.963
49.645
55.477
57.860
28
34.027
37.916
39.380
41.337
44.461
48.278
50.994
56.894
59.302
40.573
58.302
52.336
53.672
29
35.139
39.087
42.557
45.722
49.588
60.738
30
36.250
40.256
41.762
43.773
46.979
50.892
59.704
62.164
40
47.269
51.805
53.501
55.759
59.342
63.691
66.766
73.403
76.097
50
58.164
63.167
65.030
67.505
71.420
76.154
79.490
86.662
89.564
60
68.972
74.397
76.411
79.082
83.298
88.380
91.952
99.609
102.698
70
79.715
85.527
87.680
90.531
95.023
100.425
104.215
112.319
115.582
80
90.405
96.578
98.861
101.880
106.629
112.329
116.321
124.842
128.267
90
101.054
107.565
109.969
113.145
118.136
124.117
128.300
137.211
140.789
00
111.667
118.498
121.017
124.342
129.561
135.807
140.170
149.452
153.174

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