Production Line
a Quality Control Inspector Keeps a Tally Sheet

question 144

Essay

Production Line
A quality control inspector keeps a tally sheet of the number of acceptable and unacceptable products that come off two different production lines.The completed sheet is shown below. $$\begin{array}{l}\text { Products }\\\begin{array} { | c | c c | } \hline \text { Production line } & \text { Acceptable } & \text { Unacceptable } \\\hline 1 & 152 & 48 \\2 & 136 & 54 \\\hline\end{array}\end{array}$$
-Can the inspector infer at the 5% significance level that production line 1 is doing a better job than production line 2?
Hypotheses: ___________________________________
Test statistic = ________
Conclusion: ________________
Interpretation: __________________________________________________

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Definitions:

Chi-Square Statistic

Statistic that tests the difference between the distribution of observed frequencies and expected frequencies.

Expected Frequencies

The theoretical counts of occurrences across different categories or within bins that one would expect if the data followed a specific statistical distribution.

Chi-Square Statistic

A statistical measure used to determine the significance of the difference between observed and expected frequencies in categorical data.

Expected Frequencies

The anticipated count of occurrences in each category of a variable, calculated based on a theoretical distribution in the context of hypothesis testing.