Question

A χ2 goodness-of-fit test is performed on a random sample of a bag of 30 Skittles® to determine whether the proportion of each flavor (strawberry, orange, lemon, lime, and grape) is equal to the claimed amount (20% of each flavor). The χ2 statistic is determined to be 10.20. What is the p-value for this test? (4 points)

A 0.001 < p < 0.005

B 0.02 < p < 0.025

C 0.025 < p < 0.05

D 0.10 < p < 0.15

E 0.05 < p < 0.10

Answer 1

C. 0.025 < p < 0.05

Explanation:

The
`\chi^2` goodness-of-fit test parameters are presented here as follows;

The number of Skittles in the bag = 30 Skittles

The different flavors in the bag of Skittles = Strawberry, orange, lemon, lime, and grape

The number of different flavors, n = 5 flavors

The
`\chi^2` statistic = 10.20

Therefore, the degrees of freedom, d.f. = n - 1 = 5 - 1 = 4

Using the chi-square (
`\chi^2`) distribution table, we have;

The probability at 4 degrees of freedom for a
`\chi^2` statistic of 10.20 is between 0.025 and 0.05

Therefore, we get;

The probability (P > 10.20) = 0.025 < p < 0.05.