Imagine that you are hired by a manufacturing firm to investigate the effectiven
ID: 3221860 • Letter: I
Question
Imagine that you are hired by a manufacturing firm to investigate the effectiveness of three different quality control methods implemented in the production line. You randomly sample output from each quality control method and determine the proportion of defective products in each sample. You obtain the following data: You perform a chi-square test for equality of proportions and find a significant difference among the proportions. Now you wish to see which groups differ from one another. Use the multiple comparison procedure at a. 05 level of significance to determine which population proportions differ significantly. First, calculate the pairwise differences of the sample proportions: Next, compute the critical values CV_ij for each pair of proportions. Use the following table of selected values of the chi-square distribution with an alpha =. 05 level of significance and with k - 1 = 2 degrees of freedom. The chi-square value is X^2_alpha; k = 1 = _____. The critical values for the three pairwise comparison tests are: Now compare the pairwise differences of the sample proportions to the critical values to determine significance at the significance level alpha =. 05. Complete the following table:Explanation / Answer
Pairwise difference:-
|P1_P2| = 0.026, |P1_P3| = 0.142, |P2_P3| =0.168.
The critical value is 5.991. Therefore, CV12 = CV13 = CV23 = 3.841.
The table is as follows:
Comparison |Bi_Bj| CV p-value Significant Method 1 vs. Method 2 0.026 3.841 0.105376 No Method 1 vs. Method 3 0.142 3.841 0.612605 No Method 2 vs. Method 3 0.168 3.841 0.735691 No