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?

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

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.

Answer 1

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

1)

null: the number of candies follows the given distributon

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

2)

brown = 0.20

yellow

= 0.20 red = 0.10

orange = 0.10

green =0.10

blue =0.30

3)

Ho:

p_brown = 0.20

p_yellow

= 0.20 p_red = 0.10

p_orange = 0.10

p_green =0.10

p_blue =0.30

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