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: 20%20% brown, 20%20% yellow, 10%10% red, 10%10% orange, 10%10% green, and 30%30% blue. The colors present in a sample of 459459 candies was recorded. Is the representative's claim about the expected proportions of each color refuted by the data?

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 yellow. 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 0.025 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 0.025 level of significance.

Step 10 of 10: State the conclusion of the hypothesis test at the 0.025 level of significance.

Color brown yellow red orange green blue Number of Candies 44 67 67 78 44 159

Explanation / Answer

1)

null: the number of candies follows the given distributon

alternate: the number of candies does not follow the given distributon

2)

3)

Ho:

H_a: not Ho

4)

E(brown) = 459*0.2 = 91.8

5)

E(chocolate_yellow) = 0.2*459 = 91.8

6)

TS = 67.1111

7) df = r-1 = 5

8) critical value = 12.8325

9) we reject the null as TS> critical value

10) we conclude that there is sufficient evidence tat the number of candies does not follow h same proportion under null

p Oi Ei (Oi-Ei)^2/Ei 0.2 44 91.8 24.88932462 0.2 67 91.8 6.699782135 0.1 67 45.9 9.69956427 0.1 78 45.9 22.44901961 0.1 44 45.9 0.078649237 0.3 159 137.7 3.294771242 1 459 459 67.11111111 5% critical value 12.83250199 p-value 4.08586E-13

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