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, 10% red, 10% orange, 20% green, and 30% blue. The colors present in a sample of 450 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	89	89	89	44	50	89

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 0.01 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 0.01 level of significance.

Step 10 of 10: State the conclusion of the hypothesis test at the 0.01 level of significance.

Answer 1

Category	pi	Observed Freq. (Oi)	Expected Freq. (Ei)	(Oi - Ei)^2/Ei
brown	0.1	89	45	43.02
yellow	0.2	89	90	0.01
red	0.1	89	45	43.02
orange	0.1	44	45	0.02
green	0.2	50	90	17.78
blue	0.3	89	135	15.67
		450		119.53

test statistic, chi-square = 119.53

degrees of freedom   = 5

Critical value   15.086

Reject H0

The colored candies do not follow the given distribution