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The US Express reported that the color distribution for plain M&M's was: 40%brown, 20% yellow, 20% orange, 10% green, and 10% tan. Each piece of candy in a random sample of 100 plain M&M's was classified according to color, and the results are listed below.

Use a 0.05 significance level to test the claim that the published color distribution is correct.

Color Brown Yellow Orange Green Tan

Number 45      21          11     8     15

(a) Identify the null hypothesis and the alternative hypothesis.

(b) Determine the test statistic.

(c) Determine the p-value.

(d) Is there sufficient evidence to support the claim that the published color distribution is correct?

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