Question

Suppose a candy company representative claims that colored candies are mixed such that each large production batch has precisely the following proportions: 30% brown, 10% yellow, 20% red, 10% orange, 10% green, and 20% blue. The colors present in a sample of 452 candies was recorded. Is the representative's claim about the expected proportions of each color refuted by the data?

Chart: Brown goes with 72 and green goes with 112. Etc...

Color- Brown, yellow, red, orange, green, blue

Number of candies- 72, 67, 67, 67, 112, 67

Step 1: State the null and alternative hypothesis

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

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

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

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

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

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

Step 8: Find the critical value of the test at the 0.01 level of significance. Round your answer to three decimal places.

Step 9: Make the decision to reject or fail to reject the null hypothesis at the 0.01 level of significance.

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

Is or is not enough evidence to refute the company's claim about proportions of colored candies.

Answer 1

Result:

Step 1: State the null and alternative hypothesis

Ho: the proportions of candies of each color are in expected proportions

H1: the proportions of candies of each color are not in expected proportions

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

Expected proportions: 30% brown, 10% yellow, 20% red, 10% orange, 10% green, and 20% blue

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

Ho: the proportions of candies of each color are in expected proportions

H1: the proportions of candies of each color are not in expected proportions

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

135.60

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

45.20

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

161.695

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

5

Step 8: Find the critical value of the test at the 0.01 level of significance. Round your answer to three decimal places.

15.086

Step 9: Make the decision to reject or fail to reject the null hypothesis at the 0.01 level of significance.

Since calculated chi square 161.695 > critical chi square 15.086, Ho is rejected.

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

There is enough evidence to refute the company's claim about proportions of colored candies.

color	Number of candies	percentage	expected
Brown	72	30	(30/100)*452=135.60
yellow	67	10	(10/100)*452=45.20
red	67	20	(20/100)*452=90.40
orange	67	10	(10/100)*452=45.20
green	112	10	(10/100)*452=45.20
blue	67	20	(20/100)*452=90.40
	452

Goodness of Fit Test
	observed	expected	O - E	(O - E)² / E
	72	135.600	-63.600	29.830
	67	45.200	21.800	10.514
	67	90.400	-23.400	6.057
	67	45.200	21.800	10.514
	112	45.200	66.800	98.722
	67	90.400	-23.400	6.057
Total	452	452.000		161.695
	161.695	chi-square
	5	df