Suppose a candy company representative claims that colored candies are mixed suc

Question

Suppose a candy company representative claims that colored candies are mixed such that each large production batch has precisely the following proportions: 10% brown, 20% yellow, 20% red, 10% orange, 20% green, and 20% blue. The colors present in a sample of 449 candies was recorded. Is the representative's claim about the expected proportions of each color refuted by the data? Color brown yellow red orange green blue Number of Candies 72 37 82 153 37 68

Step 1 of 10: State the null and alternative hypothesis.

Step 2 of 10: What does the null hypothesis indicate about the proportions of candies of each color?

Step 3 of 10: State the null and alternative hypothesis in terms of the expected proportions for each category.

Step 4 of 10: Find the expected value for the number of chocolate candies colored brown. Round your answer to two decimal places.

Step 5 of 10: Find the expected value for the number of chocolate candies colored green. Round your answer to two decimal places.

Step 6 of 10: Find the value of the test statistic. Round your answer to three decimal places.

Step 7 of 10: Find the degrees of freedom associated with the test statistic for this problem.

Step 8 of 10: Find the critical value of the test at the 0.05 level of significance. Round your answer to three decimal places.

Step 9 of 10: Make the decision to reject or fail to reject the null hypothesis at the 0.05 level of significance.

Step 10 of 10: State the conclusion of the hypothesis test at the 0.05 level of significance.

Please include answers to each step. Thank you

Explanation / Answer

Step 1 of 10: null hypothesis:the proportions of the colored candies are precisely followed

alternate hypothesis: null hypothesis:the proportions of the colored candies are not precisely followed

please provide option for step 2 and 3

Step 4 of 10:  expected value for the number of chocolate candies colored brown =449*0.1=44.9

Step 5 of 10: Find the expected value for the number of chocolate candies colored green=89.8

Step 6 of 10:

applying chi square test:

  value of the test statistic =344.675

Step 7 of 10 degree of freedom =categories-1=5

Step 8 of 10: Find the critical value of the test =11.070

Step 9 of 10: reject Ho

Step 10 of 10: we have sufficient evidence to conclude that the proportions of the colored candies are not precisely followed

observed Expected Chi square category Probability(p) Oi Ei=total*p R2i=(Oi-Ei)2/Ei brown 0.100 72.000 44.900 16.357 yellow 0.200 37.000 89.800 31.045 red 0.200 82.000 89.800 0.678 orange 0.100 153.000 44.900 260.259 green 0.200 37.000 89.800 31.045 blue 0.200 68.000 89.800 5.292 total 1.000 449 449 344.675

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