Question

A candy company claims that their packages typically have 50 red candies, 40 yellow candies, 25 blue candies, 25 brown candies, and 10 orange candies. A study looked at a package, where it was found that the average package has 48 red candies, 42 yellow candies, 20 blue candies, 26 brown candies, and 14 brown candies. Do these observations contradict the company’s claim? Use a significant level of 0.05.

Answer 1

hypothesis:-

the packages have 50 red candies, 40 yellow candies, 25 blue candies, 25 brown candies, and 10 orange candies

at least one of the proportion is different.

here, we will do chi square test.

the necessary calculation table:-

candy colour	observed	expected
red	48	50	0.08
yellow	42	40	0.1
blue	20	25	1
brown	26	25	0.04
orange	14	10	1.6
			sum=2.82

the test statistic is:-

df = (5-1 )= 4

p value = 0.6590

[ in any blank cell of excel type =CHISQ.DIST.RT(2.42,4)press enter]

decision:-

p value = 0.6590 > 0.05 (alpha)

so, we fail to reject the null hypothesis.

conclusion:-

there is sufficient evidence to support the company's claim at 0.05 level of significance.

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