The following table contains the number of successes and failures for three cate

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 = 0.01 level of significance Failures Successes Category 1 69 71 Category 2 40 Category 3 65 78 State the hypotheses. Choose the correct answer below. O A. Ho: The categories of the variable and success and failure are independent. B. Ho: p1 = p2 = p3 ° C. Ho: The categories of the variable and success and failure are dependent 0 D. How,-E1 and 2-E2 and 3-E3 H1: The categories of the variable and success and failure are dependent. H1: At least one of th H1: The categories of the variable and success and failure are independent. H: At least one mean is different from what is expected e proportions is different from the others. What is the P-value? (Round to three decimal places as needed.) What conclusion can be made? ( A. The P-value is greater than or equal to , so reject Ho. There is not sufficient evidence that the categories of the variable and success and failure are dependent O B. The P-value is less than , so do not reject Ho There is not sufficient evidence that the proportions are different from each other O c. The P-value is less than , so reject H0. There is sufficient evidence that the proportions are different from each other ( D. The P-value is greater than or equal to , so do not reject Ho. There is sufficient evidence that the categories of the variable and success and failure are dependent.

Explanation / Answer

here for hypothesis: option B is correct

applying chi square test of independence:

p value for above test statistic =0.008

option C is correct

O category 1 category 2 category 3 Total failures 69 40 65 174 successs 71 88 78 237 Total 140 128 143 411 E=rowtotal*column total/grand total category 1 category 2 category 3 Total failures 59.270 54.190 60.540 174 successs 80.730 73.810 82.460 237 Total 140 128 143 411 =(O-E)^2/E category 1 category 2 category 3 Total failures 1.5973 3.7156 0.3285 5.641 successs 1.1727 2.7279 0.2412 4.142 Total 2.770 6.444 0.570 9.7833

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