Question

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 α=0.01

level of significance.

	Category 1	Category	Category 3
Failures	69	49	61
Successes	67	74	71

What is the​ P-value?_________​(Round to three decimal places as​ needed.)

please circle the answer

Answer 1

Ho: p1 = p2 = p3

H1: at least two proportions are unequal

Chi-Square Test of independence
	Observed Frequencies
	0
0	Category 1	Category	Category 3				Total
Failures	69	49	61				179
Successes	67	74	71				212
Total	136	123	132				391
	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	Category 1	Category	Category 3				Total
Failures	136*179/391=62.261	123*179/391=56.309	132*179/391=60.43				179
Successes	136*212/391=73.739	123*212/391=66.691	132*212/391=71.57				212
Total	136	123	132				391
	(fo-fe)^2/fe
Failures	0.7294	0.9488	0.0054
Successes	0.6159	0.8011	0.0045

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   3.105      
          
Level of Significance =   0.01      
Number of Rows =   2      
Number of Columns =   3      
Degrees of Freedom=(#row - 1)(#column -1) = (2- 1 ) * ( 3- 1 ) =   2      
          
p-Value =   0.212 [Excel function: =CHISQ.DIST.RT(χ²,df) ]  
Decision:    p value > α , do not reject Ho