Question

A manufacturer of colored candies states that 13% of the candies in a bag should be brown, 4% yelow 13% rad, 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 obtainad the results shown in the table. Tes: whether the bag of colores candies follows the distribution stated above at the x = 0.05 level of significanos Click the icon to view the table. Determine the null and alternative hypotheses. Choose the correct answer below. O A. H. The distribution of colors is not the same as stated by the manufacturer. H: The distribution of colors is the same as slaled by the manufacturer. B. H. The distribution of colors is the same as stated by the manufachurer. He: The distribution of colors is not the same as stated by the tranufacturer. i Observed Distribution of Colors OC. None of these Compute the expected counts for each color. Color Frequency Expected Count Brown GO Color Frequency Cialmed Proportion Calored Candles in a bag ErVATI Yellon Red Blue 60 64 54 63 0.13 0.14 0.13 0.24 Orange Green 81 65 0.20 0.16 Yellow 614 51 Red Blue Print Done 63 a1 Orange Green Ei! (Round to two decimal paces se needed.) What is the best seletic? 2-06 (Round to three decimal places as needed What is the P-value of the test? P value = a Round ta three decimal places as needed.) Based on the resulls, do the colors lo low he saire dis.ribution assisted in the problern? A. Reject Hy. There is not sufficient evidence that the distribution of colors is not the same as stated by the manufacturer. B. Do not reject Ho. There is not eufficient evidence that the dietribution of colors is not the same as stated by the manufacturer. OC Do not miest Ho. There is sufficient avidence that the distribution of colors is not the same as stated by the manufacturer D. Reject Hg. There is sullicieril evidence that the cistribulion of colors is not the same as slated by the inarulaclurer.

Answer 1

Solutions Hypothesis Ho. The distribution of colours is Same as stated by Manufasen Ha: The distribution of Colours is not the same as stated. opton B colour Frequency Proportion (P) Eupected Count E=nxp 60 013 So.31 Brown Yellow 64 0.14 54.18 50.31 S4 0.13 92.88 Red Blue 0.24 63 77.4 Orange 81 0:20 Green 65 0.16 61.92 n=387

Chi-Square Calculator - Results Expected Chi-Square Component Observed Categories O; Ei (0;- E;)2 / E Category 1 60 50.31 1.8664 Category 2 64 54.18 1.7799 Category 3 54 50.31 0.2706 Category 4 63 92.88 9.6126 Category 5 81 77.4 0.1674 Category 6 65 61.92 0.1532 Total: 387 387.00000000000006 13.8501

Test statistic(X²) = 13.8501

P value = 0.01659

since p value is less then 0.05

Reject H0, Their is sufficient evidence to support claim.

Option D