Question

partial credit, 12.1.11-T 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 the alpha equals0.05 level of significance. Determine the null and alternative hypotheses. Choose the correct answer below. A. H0​: The distribution of colors is not the same as stated by the manufacturer. H1​: The distribution of colors is the same as stated by the manufacturer. B. H0​: The distribution of colors is the same as stated by the manufacturer. H1​: The distribution of colors is not the same as stated by the manufacturer. C. None of these. Click to select your answer and then click Check Answer. 4 parts remaining Observed Distribution of Colors Colored Candies in a bag Color Brown Yellow Red Blue Orange Green Frequency 61 64 52 63 96 66 Claimed Proportion 0.13 0.14 0.13 0.24 0.20 0.16 What is the test​ statistic? chi Subscript 0 Superscript 2 equals ​(Round to three decimal places as​ needed.) What is the​ P-value of the​ test? ​P-valueequals ​(Round to three decimal places as​ needed.) Based on the​ results, do the colors follow the same distribution as stated in the​ problem? A. Do not reject Upper H 0. There is sufficient evidence that the distribution of colors is not the same as stated by the manufacturer. B. Do not reject Upper H 0. There is not sufficient evidence that the distribution of colors is not the same as stated by the manufacturer. C. Reject Upper H 0. There is sufficient evidence that the distribution of colors is not the same as stated by the manufacturer. Your answer is correct.D. Reject Upper H 0. There is not sufficient evidence that the distribution of colors is not the same as stated by the manufacturer.

Answer 1

The  null and alternative hypotheses are,

B. H0​: The distribution of colors is the same as stated by the manufacturer.

H1​: The distribution of colors is not the same as stated by the manufacturer.

Observed Distribution of Brown, Yellow, Red, Blue, Orange and Green Colors are

61, 64, 52, 63, 96, 66

Total number of candies = 61 + 64 + 52 + 63 + 96 + 66 = 402

Expected Distribution of Brown, Yellow, Red, Blue, Orange and Green Colors are

402 * 0.13, 402 * 0.14, 402 * 0.13, 402 * 0.24, 402 * 0.20, 402 * 0.16

52.26, 56.28, 52.26, 96.48, 80.40, 64.32

chi Square test statistic =

= (61 - 52.26)² / 52.26 + (64 - 56.28)² / 56.28 + (52 - 52.26)² / 52.26 + (63 - 96.48)² / 96.48 + (96 - 80.40)² / 80.40 + (66 - 64.32)² / 64.32

= 17.211

Degree of freedom = k - 1 = 6 - 1 = 5 (k is number of types of candies)

P-value of the​ test = P( > 17.211, df = 5) = 0.004

Since p-value is less than 0.05 significance level, we reject null hypothesis H0 and conclude that there is significant evidence that the distribution of colors is not the same as stated by the manufacturer.

C. Reject Upper H 0. There is sufficient evidence that the distribution of colors is not the same as stated by the manufacturer.