A manufacturer of colored chocolate candies specifies the proportion for each co

Question

A manufacturer of colored chocolate candies specifies the proportion for each color on its website. A sample of randomly selected 100 candies was taken, with the following result:

(a) Which hypotheses should be used to test if the sample is consistent with the company's specifications:
H0:

-p1 = 11, p2 = 11, p3 = 8, p4 = 19, p5 = 21, p6 = 30

-p1 = p2 = p3 = p4 = p5 = p6 = 1/6

-p1 = 0.23, p2 = 0.21, p3 = 0.15, p4 = 0.13, p5 = 0.13, p6 = 0.15

-p1 = p2 = p3 = p4 = p5 = p6 = 0 ,

Ha:

-all of the p's are different from the specified values

-at least one of the p's is different from the specified values

(b) Calculate the expected count for each color: (use 2 decimals.)
Blue:  
Orange:  
Green:  
Brown:  
Red:  
Yellow:  

(c) Which condition(s) are met for doing a chi-squared test?

-The sample was randomly selected.

-None of the conditions are met.

-It it reasonable to assume the candies are independent of each other.

-The expected count is at least 5 for every cell.

(d) How many degrees of freedom are there?  

(e) Calculate the contribution to the test statistic for Blue: (use 2 decimals.)  

Color Blue Orange Green Brown Red Yellow Specified % 23% 21% 15% 13% 13% 15% Observed count 11 11 8 19 21 30

Explanation / Answer

(a) H0 : p1 = 0.23, p2 = 0.21, p3 = 0.15, p4 = 0.13, p5 = 0.13, p6 = 0.15

Ha: at least one of the p's is different from the specified values

(b) Expected count

(c) All three conditions are met here.

(d) Degree of freedom here = (6 -1) = 5

(e) Test statsitic for blue = (11 -23)2 / 23 = 6.26

Color Expected (E) Blue 23 Orange 21 Green 15 Brown 13 Red 13 Yellow 15 100

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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