Question

1. The Jupiter Candy Company claims their Good and Colorful candies are distributed by color as follows: Turquoise: 12%; Maroon: 21%; Chartreuse: 28%; Burnt Sienna: 14%; Eggshell: 25% A random sample of 200 G and C’s resulted in the following counts: Turquoise: 20; Maroon: 45; Chartreuse: 40; Burnt Sienna: 32; Eggshell: 63 Test whether the candies follow the given distribution at the level of significance (α) of 0.05

Answer 1

The Hypothesis

H0: The Jupiter Candy color is distributed as follows Turquoise = 12%, Maroon = 21%, Chartreuse = 28%, Burnt = 14%, Eggshell = 25%

Ha: The distribution differs from that stated in the null hypothesis.

The Test Statistic:

Each Expected value = (% / 100) * N. N = 200

	Observed	Expected %	Expected	(O-E)2	(O-E)2/E
Turquoise	20	12	24	16	0.66670
Maroon	45	21	42	9	0.21430
Chartreuse	40	28	56	256	4.57140
Burnt	32	14	28	16	1.00000
Eggshell	63	25	50	169	3.00000
Total	200.00	100.00	200.00		9.45

Test = 9.45

The Critical value at = 0.05, df = n – 1 = 4, critical = 9.488

The p value Foe Test = , for df = n – 1 = 4, p value = 0.0507

The Decision Rule: If test is > critical, then Reject H0.

If p value is < , Then Reject H0.

The Decision:   Since test (9.45) is < critical (9.488), We Fail to reject H0.

Since p value (0.0507) is > (0.05), We Fail To Reject H0.

The Conclusion: There isn't sufficient evidence at the 95% significance level to warrant rejection of the claim that the candies follow the given distribution.

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