Question

A manufacturer of colored candies states that 13% of the candies in a bag should be brown, 14% yellow, 13% red, 24% blue, 20% orange, and 16% groen. A student randomly selected a bag of colored candies. He counted the number of candies of each color and obtained the results shown in the table Test whether the bag of colored candies follows the distribution stated above at the a=0.05 level of significance. Click the icon to view the table Rew www wyr He: The distribution of colors is not the same as stated by the manufacturer OB. Hy: The distribution of colors is not the same as stated by the manufacturer H: The distribution of colors is the same as stated by the manufacturer OC. None of these Compute the expected counts for each color Color Frequency Expected Count Brown 59 51.00 Yellow 65 55.02 Red 50 51.00 Blue 80 9432 Orange 90 78.60 Green 63 62.88 (Round to two decimal places as needed.)

find the test statistic and p - value

also based on the results do the colors follow the same distibution as stated in thr problem?

Answer 1

H0:	The distribution of colors is same as the stated by the manufacturer
H1:	The distribution of colors is not same as the stated by the manufacturer
Level =	0.05
	CALCULATION TABLE
	O	E	O-E	(O-E)2/E
BR	59	51.09	7.91	1.224664318
Y	65	55.02	9.98	1.810258088
R	56	51.09	4.91	0.471875122
BL	60	94.32	-34.32	12.48793893
O	90	78.6	11.4	1.653435115
G	63	62.88	0.12	0.000229008
SUM =	393	71	0	17.64840058
Chi sq test statistics=	17.648
DF= 5
p value=  0.003422
Conclusion:	p value( 0.003422)  < 0.05
	Reject Ho
so we conclude that	The distribution of colors is not same as the stated by the manufacturer

What is the test statistic? xo 17.648 (Round to three decimal places as needed.) What is the P-value of the test? P-value = round to three decimal places as needed.) Based on the results, do the colors follow the same distribution as stated in the problem? OB. Reject Ho. There is sufficient evidence that the distribution of colors is not the same as stated by the manufacturer.

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