A Manufacturing Company Produces Part A732 for the Aerospace Industry

Multiple Choice

A manufacturing company produces part A732 for the aerospace industry.This particular part can be manufactured using 3 different production processes.The management wants to know if the quality of the units of part A732 is the same for all three processes.The production supervisor obtained the following data: Process 1 had 29 defective units in 240 items,Process 2 produced 12 defective units in 180 items,and Process 3 manufactured 9 defective units in 150 items.
Chi-Square Contingency Table Test for Independence $\begin{array}{c}\begin{array}{lll}\text { } \\\text { Row 1 } \\ \text { } \\\text { } \\\text { Row 2} \\\text { } \\\text { } \\\text { Total } \\\text { } \\\text { } \\\end{array}\begin{array}{l}\text { } \\\hline \text { Observed } \\\hline \text { Expected } \\\hline(\mathrm{O}-\mathrm{E}) ^{2} / \mathrm{E} \\\hline \text { Observed } \\\hline \text { Expected } \\\hline(\mathrm{O}-\mathrm{E}) ^{2} / \mathrm{E} \\\hline \text { Observed } \\\hline \text { Expected } \\\hline(\mathrm{O}-\mathrm{E}) ^{2} / \mathrm{E}\end{array}\begin{array}{|l|}\text { Col } 1\\\hline 29 \\\hline 21.05 \\\hline 3.00 \\\hline 211 \\\hline 218.95 \\\hline 0.29 \\\hline 240 \\\hline 240.00 \\\hline 3.29 \\\end{array}\begin{array}{l}\text { Col } 2\\\hline 12 \\\hline 15.79 \\\hline 0.91 \\\hline 168 \\\hline 164.21 \\\hline 0.09 \\\hline 180 \\\hline 180.00 \\\hline 1.00 \\ \end{array}\begin{array}{|l|}\operatorname{Col} 3\\\hline 9 \\\hline 13.16 \\\hline 1.31 \\\hline 141 \\\hline 136.84 \\\hline 0.13 \\\hline 150 \\\hline 150.00 \\\hline 1.44 \\ \end{array}\begin{array}{r}\text { Total } \\\hline 50 \\\hline 50.00 \\\hline 5.22 \\\hline 520 \\\hline 520.00 \\\hline 0.50 \\\hline 570 \\\hline 570.00 \\\hline 5.73 \end{array}\end{array}$

$\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\begin{array}{cc}5.73 & \text { chi-square } \\.0571 & \text { p-value }\end{array}$

At a significance level of .05,the management wants to perform a hypothesis test to determine if the quality of the items produced appears to be independent of the production process used.Based on the results summarized in the MegaStat/Excel output provided in the table above,we:

A) Reject H₀ and conclude that the quality of the product is not the same for all processes.
B) Reject H₀ and conclude that the quality of the product is dependent on the manufacturing process.
C) Do not reject H₀,and conclude that the quality of the product does not significantly differ among the three processes.
D) Do not reject H₀,and conclude that the quality of the product is not the same for all processes.
E) Reject H₀ and conclude that the quality of the product is independent of the manufacturing process used.