Question

A 1-pound bag of candy-coated chocolate-covered peanuts contained 224 pieces of candy, each colored brown, orange, green, or yellow. Test the null hypothesis that the machine filling these bags treats the four colors of candy equally likely; that is, test H0 : pB = pO = pG = py = 1 4 The observed values were 42 brown, 64 orange, 53 green, and 65 yellow candies. You may select the significance level or give an approximate p-value.

Answer 1

The colours are equally likely is the conclusion.

Explanation:

Given that a 1-pound bag of candy-coated chocolate-covered peanuts contained 224 pieces of candy, each colored brown, orange, green, or yellow.

`H_0: all colours are equaly likely\\\\H_a: atleast two colours are not equally likely`

(Two tailed chi square test)

We assume H0 to be true and find the expected frequencies. Then calculate chi square and check the p value

Orangw Brown Green Yellow

Observed 64 42 53 65 224

Expected 56 56 56 56 224

O-E 8 -14 -3 9

chisqurae 1.142857143 3.5 0.160714286 1.446428571 6.25

df 3

p value =0.1000

let us assume alpha is 5%

since p value is >5% we accept H0

The colours are equally likely is the conclusion.