12.1
6. A manufacturer of colored candies states that 13% of the candies in a bag should be brown, 14% yellow, 13% red, 24% blue, 20% orange, and 16% green. A student randomly selected a bag of colored candies. He counted the number of candies of each color and obtained the results shown in the table. Test whether the bag of colored candies follows the distribution stated above at a = 0.05 level of significance. Using the level of significance a = 0.05, test whether the color distribution is the same. Click here to view the table.' Click here to view the table of critical values of the chi-square distribution.2 Determine the null and alternative hypotheses. Choose the correct answer below. A. Ho: The distribution of colors is not the same as stated by the manufacturer. H,: The distribution of colors is the same as stated by the manufacturer. O B. Ho: The distribution of colors is at most as uniform as stated by the manufacturer. H,: The distribution of colors is more uniform than stated by the manufacturer. C. Ho: The distribution of colors is the same as stated by the manufacturer. 1: The distribution of colors is not the same as stated by the manufacturer. O D. Ho: The distribution of colors is at least as uniform as stated by the manufacturer. H: The distribution of colors is less uniform than stated by the manufacturer. Compute the expected counts for each color Color Frequency Expected Count Brown 61 Yellow 67 Red 56 Blue 60 Orange 94 Green 65 (Round to two decimal places as needed.) What is the test statistic? XO = Round to three decimal places as needed.) What is the range of P-values of the test? The range of P-values of the test is (1) Based on the results, do the colors follow the same distribution as stated in the problem? O A. Do not reject Ho. There is sufficient evidence that the distribution of colors is not the same as stated by the manufacturer. O B. Reject Ho. There is not sufficient evidence that the distribution of colors is not the same as stated by the manufacturer. O C. Reject Ho. There is sufficient evidence that the distribution of colors is not the same as stated by the manufacturer O D. Do not reject Ho. There is not sufficient evidence that the distribution of colors is not the same as stated by the manufacturer. 1: Observed Distribution of Colors Colored Candies in a bag Color Brown Yellow Red Blue Orange Green Frequency 61 67 56 60 94 65 Claimed Proportion 0.13 0.14 0.13 0.24 0.20 0.16 2: Chi-Square Distribution Critical Values Table Chi-Square (x ) Distribution Degrees of Areato the Right of Critical Value Freedom 0.995 0.99 0.975 0.9 0.90 01 0.05 0.025 0.01 0.005 0.001 0.004 0.016 2.706 3.841 5.024 6.635 7879 0.010 0.020 0.061 0,10 0.21 4.605 $991 7.378 10.597 0.072 0115 0.216 0.352 0.584 6.251 7815 9.348 11.345 12.838 0.207 1297 0.484 0.711 1.064 7.779 9488 11.143 13.27 14.860 0.412 0554 0.831 1.145 1.610 9.236 11.070 12.833 15.08 16.750 0.676 0.872 1.237 1.635 2.204 10.64 12.59 14.449 6.81 18.54 0.989 1.239 1.690 2,167 2.833 12.017 14.067 16.013 18.47 20 278 1.344 1.646 2180 2.164 2,733 3.490 15.507 17535 20.090 21.955 1.735 2.088 2.70 3.325 4.168 14.684 16.919 19.023 21.656 23589 2.156 2.358 3.247 3 94 4.865 15.987 18.307 20.483 23209 25.188 2603 3.063 3.816 4.575 19.675 24 725 25357 3074 3.571 5.226 6.304 18.549 21.02 23.337 26 217 8.300 3.565 4.107 4.40 5 892 7042 19.812 22.362 24.736 29 819 4075 4.660 5.62 6.571 7.790 21.064 23.685 25.119 29141 31.319 4601 5.229 6.262 7261 8.547 22.307 24.996 27.488 30578 32.801 5.142 5.812 6.908 9.312 23.542 26.29 28.84 3200 34.267 5.697 6.408 7564 8.672 10.08 24.769 27587 30.191 33.40 35.718 6.265 7015 8.231 9.390 10.865 25 989 28.869 30 144 31.52 34.805 37156 6.844 7633 8 907 10.117 11.651 27204 32.852 36.191 38.582 7434 8.260 9.591 10.851 12.443 28.412 31.410 34.170 37566 39.997 8.034 8.897 10.283 11.591 13.240 29.615 32.67 35.479 38 932 41.401 8.643 9.542 10.982 12.338 14.041 30.813 33.92 36.781 40.28 42.796 9.260 10196 13.091 32.00 38.076 44.181 9.886 1085 12.401 13.848 15.659 33.19 36.415 39.36 4298 45.559 10.520 11.52 13.120 14.611 16.473 34.38 37652 40.646 44.314 46.928 11.160 2198 3.844 15.379 17.292 35.563 38.885 41.92 45.64 48.290 11808 12879 14.573 16.151 18.114 36.741 40.11 43.19 16.96 49 645 1246 13127 13.565 15.308 16.928 18.939 37916 44.461 48 378 50993 14.256 16.047 17.708 19.768 4255 45.722 49.588 13.78 14.953 16.791 18.49 20.599 40.256 43.773 46.979 50.892 53672 20.70 22.164 24.433 26.509 29 051 $1.80 55.75 59.34 53 69 66 766 9.707 32.357 34.764 37689 63.16 5750 76.154 35 53 40.482 43.188 46.459 71.420 74.397 79.082 83.298 88.379 43275 45.442 48.758 $1.739 $5.329 85.52 90.531 95.023 100.425 $1.17 53.540 57153 60.391 64.278 96.578 101.879 106.629 112.329 59.19 61.754 65.647 69.126 73.29 107.565 113.145 118.136 124.116 128.299 100 67.328 70.065 74.222 77929 82.358 118.498 124.342 129.561 135 807 140.169 Left tail Right tail -Area = 1-& Two tails The area to the Xi- The area to the The area to the right night of this right of this value is av. of this value is, value is 1-a The area to the right of this value is 1 - . (1) O between 0.05 and 0.10. O less than 0.01. between 0.025 and 0.05. between 0.01 and 0.025. greater than 0. 10
