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...

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.

1. Establish two working hypotheses, namely null-hypothesis, , and alternative hypothesis, .


2. Use a Chi-square distribution to test the goodness-of-fit between the sample statistics


3. Account for the degrees of freedom


4. Using the degrees of freedom estimate a critical value for testing the sample statistics at a 99% confidence level (1% level of significance)


5. Conclude the test and interpret the conclusion

Table 1. Categories in a union survey

Table 2. Survey responses new survey

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

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Extracted text: 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