1. There are five different colors of original Skittles candies: purple, yellow,

Question

1. There are five different colors of original Skittles candies: purple, yellow, green, orange, and red. Assume that in the population, Skittles are mixed so that there are equal proportions of each color (i.e., 20% of each color).

If we repeatedly take samples of n=100 from that population and test the null hypothesis that the proportions are all equal using a chi-square goodness-of-fit test, which of the following statements is true? Explain why.

              A. You will get a p-value less than 0.05 every time.

              B. You will get a p-value greater than 0.05 every time.

              C. You will get a p-value less than 0.05 about 5% of the time.

What do you think the distribution of p-values would look like if you were to carry out the simulation described in question 1? Explain why.

Explanation / Answer

Correct Answer: B. You will get a p-value greater than 0.05 every time.

Simulation:

From simulation data, we prepare table with observed frequencies

Num Categories: 5
Degrees of freedom: 4
Expected Freq: 20

Test Statistic, X^2: 2.3000
Critical X^2: 9.48772
P-Value: 0.6808

Here P-value > alpha 0.05, so we accept H0

Thus , we conclude that the simulation data is follows with equal proportions

Observed Expected Color Freq (Oi) Probability Freq Ei (Oi-Ei)^2 /Ei Purple 24 0.20 20 0.8 Yellow 22 0.20 20 0.2 green 16 0.20 20 0.8 ornage 17 0.20 20 0.45 Red 21 0.20 20 0.05 Total: 100 100 2.3

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