A manufacturer of colored chocolate candies specifies the proportion for each co
ID: 3309882 • Letter: A
Question
A manufacturer of colored chocolate candies specifies the proportion for each color on its website. A sample of randomly selected 101 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: Pick one of the options in each set of parentheses.
H0: ( p1 = 9, p2 = 21, p3 = 20, p4 = 30, p5 = 10, p6 = 11 OR p1 = p2 = p3 = p4 = p5 = p6 = 0 OR p1 = p2 = p3 = p4 = p5 = p6 = 1/6 OR p1 = 0.17, p2 = 0.12, p3 = 0.12, p4 = 0.15, p5 = 0.21, p6 = 0.23) , implying the sample is (consistent OR inconsistent) with the company's specifications.
Ha: (at least one of the p's is different from the specified values OR all of the p's are different from the specified values) , implying the sample is (inconsistent OR consistent) with the company's specifications.
(b) Calculate the expected count for each color: (use 2 decimals.)
Green:
Brown:
Red:
Yellow:
Orange:
Blue:
(c) Are the conditions met for doing a chi-squared test? Select all that apply.
___ It it reasonable to assume the candies are independent of each other.
___ The sample was randomly selected.
___ None of the conditions are met.
___ 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 Green: (use 2 decimals.)
(f) For this sample, the P-value is 0.001. What is the conclusion of the hypothesis test, for = 0.05? Pick one of the options in each set of parentheses.
(Reject H0 OR Do not reject H0) .There is (sufficient OR insufficient) evidence the sample is (inconsistent OR consistent) with the company's specifications.
Explanation / Answer
a)Ho: p1 = 0.17, p2 = 0.12, p3 = 0.12, p4 = 0.15, p5 = 0.21, p6 = 0.23 implying the sample is consistent with the company's specifications.
Ha: (at least one of the p's is different from the specified values implying the sample is inconsistent with the company's specifications.
b)as expected count =% *total
hence
c)it is reasonable to assume the candies are independent of each other.
The sample was randomly selected.
The expected count is at least 5 for every cell.
d) degrees of freedom =cateories-1 =6-1=5
e) contribution to the test statistic for Green =()bserved-expected)2/expected count =3.89
f) for p value is less then 0.05 level
Reject H0 There is sufficient evidence the sample is inconsistent with the company's specifications.
face E=total*p green 17.17 Brown 12.12 red 12.12 Yellow 15.15 Orange 21.21 Blue 23.23Related Questions
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