Question

Conduct the hypothesis test and provide the test statistic and the critical? value, and state the conclusion.

A company claims that its packages of 100 candies are distributed with the following color? percentages:

13?% red, 22?%? orange, 16?%? yellow, 8?%? brown, 23?% blue, and 18?% green. Use the given sample data to test the claim that the color distribution is as claimed. Use a

0.10 significance level.

candy count

color	number in package
red	12
orange	25
yellow	8
brown	10
blue	27
green	18

The test statistic is ... (Round to two decimal places as needed)

The critical value is ... (Round to three decimal places as needed.)

The P-value is ... (Round to three decimal places as needed.)

State the conclusion.

Do not reject OR Reject H0. There is not OR is sufficient evidence to warrant rejection of the claim that the color distribution is as claimed.

Answer 1

1) A company claims that its packages of 100 candies are distributed with the given color percentages.

Therefore,

Null Hypothesis, H₀ : There is not sufficient evidence to warrant rejection of the claim that the color distribution is as claimed.

Alternate Hypothesis, H₁ : There is sufficient evidence to warrant rejection of the claim that the color distribution is as claimed.

Color (x)	Probability P(x)	Number in package (Observed Frequency, Oi)	Expected frequency (Ei)
Red	0.13	12	13	0.0769
Orange	0.22	25	22	0.4091
Yellow	0.16	8	16	4.0000
Brown	0.08	10	8	0.5000
Blue	0.23	27	23	0.6957
Green	0.18	18	18	0
Total	1	100	100

Test statistic is

Therefore the value of the test statistic is,

Therefore, the value of test statistic is 5.68.

2)

Here, n=6 and n - 1 = 5

Let the level of significance = =0.10

Therefore the critical value is,

The above value is obtained from the Chi-square table.

3)

The P-value is obtained by using the following formula

The above probability is obtained from Excel using "CHIDIST(5.68,5)".

Therefore the P-value is 0.339.

4)

Since P-value = 0.339 > level of significance = = 0.10, therefore we can not reject H₀ at 10 % level of significance and conclude that there is not sufficient evidence to warrant rejection of the claim that the color distribution is as claimed.

Reference: Chi-square Table