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A Manufacturing Company Produces Part A732 for the Aerospace Industry

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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   Row 1    Row 2   Total     Observed  Expected (OE) 2/E Observed  Expected (OE) 2/E Observed  Expected (OE) 2/E Col 12921.053.00211218.950.29240240.003.29 Col 21215.790.91168164.210.09180180.001.00Col3913.161.31141136.840.13150150.001.44 Total 5050.005.22520520.000.50570570.005.73\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 5.73 chi-square .0571 p-value \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:

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Definitions:

Cocktail Party Phenomenon

The ability of individuals to focus their attention on a single conversation in a noisy environment, filtering out other conversations.

Phi Phenomenon

An optical illusion of perceived continuous motion between separate objects viewed rapidly in succession, such as in motion pictures.

Name-Orientation Response

The behavior in which an individual reacts to hearing their name, often used as an indicator of attention or awareness.

Subliminal Perception

The processing of information by sensory systems without conscious awareness, typically used in the context of subliminal messages.

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