Question

Conduct the hypothesis test and provide the test​ statistic, critical value and​ P-value, and state the conclusion.

A package of 100 candies are distributed with the following color​ percentages: 15​% ​red, 20​% orange,16​% yellow, 10​% brown, 25​% blue, and 14​% green.

Use the given sample data to test the claim that the color distribution is as claimed. Use a 0.025 significance level.

Candy counts:

Color	Number in Package
Red	15
Orange	23
Yellow	6
Brown	9
Blue	27
Green	20

The test statistic is: (Round to two decimal places):

The critical value is (Round to three decimal places):

The P-value is (Round to three decimal places):

State the Conclusion:

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

Answer 1

using minitab>stat>tables >chi square

we have

Chi-Square Goodness-of-Fit Test for Observed Counts in Variable: Number in Package

Using category names in Color

Test Contribution
Category Observed Proportion Expected to Chi-Sq
Red 15 0.15 15 0.00000
Orange 23 0.20 20 0.45000
Yellow 6 0.16 16 6.25000
Brown 9 0.10 10 0.10000
Blue 27 0.25 25 0.16000
Green 20 0.14 14 2.57143

N DF Chi-Sq P-Value
100 5 9.53143 0.090

Data
Level of Significance	0.025
Degrees of Freedom	4
Critical Value	11.14329

The test statistic is: 9.53

The critical value is 11.143

The P-value is 0.090

State the Conclusion:

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