A bag of candy contains 5 different types of colored candies; red, green, blue, yellow, and orange.

Milla Werner

Milla Werner

Answered question

2022-03-04

A bag of candy contains 5 different types of colored candies; red, green, blue, yellow, and orange. According to the manufacturer, bags should contain an equal number of each color. Students in a statistics class decided to use a chi-square procedure to test the manufacturer’s claim. They opened a bag of candy and recorded the number of candies of each color. The results are shown in the following table.
 Red  Green  Blue  Yellow  Orange 1724202514
Which color contributes most to the chi-square test statistic?
a. Red
b. Green
c. Blue
d. Yellow
e. Orange

Answer & Explanation

Kathryn Duggan

Kathryn Duggan

Beginner2022-03-05Added 7 answers

The null and alternative hypotheses are stated below:
H0: P1= P2= P3= P4= P5=1/5.
Hα: At least one Piis not equal to 0.20.
The chi-square test is appropriate in this situation.
The test statistic is given below:
χ2=(OiEi)2Eiχ{(k1)}2
Where Oi=Observed frequency, Ei= Expected frequency, k= Number of observations
The Expected frequencies and test statistics can be obtained as follows:
OiEi(OiEi)2/Ei Red 1720(=100×0.20)0.45 Green 2420(=100×0.20)0.8 Blue 2020(=100×0.20)0 Yellow 2520(=100×0.20)1.25 Orange 1420(=100×0.20)1.8 Total 100100
From the above table, it is clear that (OiEi)2Ei is high for orange.
Thus, orange contribute most to chi-square test statistics.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?