1. A particular brand of candy-coated chocolate comes in five different colors t

Question

1. A particular brand of candy-coated chocolate comes in five different colors that we shall denote as Ai = {brown), A2 {yellow}, A3 {orange), A4 = {green), and As cof fee). Let p equal the probability that the color of a piece of candy selected at random belongs to A,i-1,2, ..,5. Test the null hypothesis Ho Pi = 0.4, P2 = 0.2,Pa = 0.2, p. = 0.1, P5 = 0.1 using a random sample of n 580 pieces of candy whose colors yielded the respective frequencies 224, 119, 130, 48, and 59. Use the significance level 5%, approximate p-value.

Explanation / Answer

Here we use the goodness of fit test.

The Hypothesis:

H0: There is no difference between the observed and expected frequencies.

Ha: There is a difference in observed and expected frequencies.

The Test statistic: The below table show the calculation of the test Statistic.

2test = 3.78

The p Value:   The p value at 2test = 3.78 , df = n -1 = 5 - 1 = 4 is

p value = 0.4366

The Decision Rule: If p value is < , then Reject H0.

The Decision:    Since If p value (0.4366) is > (0.05), We Reject/Fail to reject H0.

The Conclusion: There is insufficient evidence at the 95% significance level to conclude that there is a difference in observed and expected frequencies.

Observed Expected % Expected (O-E)2 (O-E)2/E A1 224 40 232 64 0.275862 A2 119 20 116 9 0.077586 A3 130 20 116 196 1.689655 A4 48 10 58 100 1.724138 A5 59 10 58 1 0.017241 Total 580.00 100.00 580.00 370.00 3.78

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.