the following table contains the number of successes and failures for three categories of a variable....

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the following table contains the number of successes and failures for three categories of a variable. Test whether the proportions are equal for each category at the a=.1 level of signifcance.

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Failures Successes Category 1 Category 2 Category 3 90 66 38 32 59 40

State the hypotheses. Choose the correct answer below. O A. Ho: P1 P2 P3 H, At least one of the proportions is different from

What is the P-value? (Round to three decimal places as needed) What conclusion can be made? O A. The P value is less than a s

math Statistics-And-Probability

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Answer 1

Answer #1

OA. Ho: P1 P2 P3 He: At least one of the proportions is different from the others.

Applying chi square test of homogeneity

Expected	E_i=row totalcolumn total/grand total*	Category 1	Category 2	Category 3	Total
	Failures	72.8246	74.6154	46.5600	194
	Success	49.1754	50.3846	31.4400	131
	total	122	125	78	325

chi square χ²	=(O_i-E_i)²/E_i	Category 1	Category 2	Category 3	Total
	Failures	4.051	0.995	1.574	6.6193
	Success	5.999	1.473	2.331	9.8026
	total	10.0496	2.4679	3.9043	16.4218

test statistic X²=		16.422
p value =	0.000	*from excel: chidist(16.4218,2)*

O A. The P value is less than , so reject H. There is sufficient evidence that the proportions are different from each other.

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Answer 2

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