Question 1 (6 points) Chicken Delight claims that at least 90 percent of its ord

Question

Question 1      (6 points)

Chicken Delight claims that at least 90 percent of its orders are delivered within 7 minutes of the time the order was placed. To test that claim, you collect a sample of 67 orders. Using a level of significance of 0.05, what is the highest possible number of orders that were delivered within 7 minutes that would lead to the rejection of Chicken Delight’s claim? Show your work!

Question 2      (5 points)
A bag of M&M's Peanut Butter and Almond is supposed to have 20% each of the following colors: brown, yellow, green, blue, and red. In a bag of 100 M&M’s, you find the following color distribution:

22 brown, 17 yellow, 18 green, 13 blue, and 30 red. Using a significance level of 0.05, test the null hypothesis that there is no meaningful difference between the observed and expected frequencies.

*** Continued on p. 2 ***

Question 3      (4 points)

Please state what you think is the most important technique that you learned about in this course and give one example of 100 words or more of how you think that it may be used in the area of business you plan to go into after graduation.

Explanation / Answer

Question 1:
Ho: p >= 0.90
Ha: p < 0.90

n = 67

= sqrt[ P * ( 1 - P ) / n ], where P = 0.9
= 0.03665

For 0.05 significance level and one sided test, z = -1.645

z = (p - P) / = -1.645
(p - 0.9)/0.03665 = -1.645, p = 0.84

Question 2:

For a chi-square goodness of fit test, the hypotheses take the following form.

H0: there is no meaningful difference between the observed and expected frequencies.
Ha: there is a meaningful difference between the observed and expected frequencies.

Observed Counts are: Brown: 22, Yellow: 17, Green: 18, Blue: 13, Red: 30
Expected Counts are: Brown: 20, Yellow: 20, Green: 20, Blue: 20, Red: 20

Degree of freedom, df = k - 1 = 5 - 1 = 4

Test Statistic, 2 = [ (Oi - Ei)2 / Ei = [22 - 20]2/20 + [17 - 20]2/20 + [18 - 20]2/20 + [13 - 20]2/20 + [30 - 20]2/20
= 8.3

p-value = The P-Value is 0.0812 > 0.05, Fail to reject null hypothesis. there is no meaningful difference between the observed and expected frequencies.

H0: there is no meaningful difference between the observed and expected frequencies.
Ha: there is a meaningful difference between the observed and expected frequencies.

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