A researcher claims that the number of different-colored candies in bags of peanut M&M’s^® is uniformly distributed. To test this claim, you randomly select a bag that contains 180 peanut M&M’s^®. The results are shown in the table given below. Using α = 0.05, test the researcher’s claim.

a. Verify that the expected frequency is at least 5 for each category.

b. Identify the expected distribution and state H₀ and H_a.

c. Identify the level of significance α.

d. Identify the degrees of freedom.

e. Find the critical value X₀² and identify the rejection region.

f. Find the chi-square test statistic. Sketch a graph.

g. Decide whether to reject the null hypothesis.

h. Interpret the decision in the context of the original claim.

Color              Frequency, f

Brown ……………..  22

Yellow …………….   27

Red ………………..    22

Blue ……………….    41

Orange …………….  41

Green ……………...  27