A supplier of laptop PC power supplies uses a control chart...

A supplier of laptop PC power supplies uses a control chart to track the output (in watts) of each unit produced. The pattern below shows whether each unit's output was above $(A)$ or below $(B)$ the desired specification. Research question: At $\alpha=.05$, do the deviations follow a random pattern? [.] Watts $B A A B B B A B A B A A B A B B A B B A A B A B A$ AA B BAA AA B BAA BAA AAB BAABAA

A supplier of laptop PC power supplies uses a control chart to track the output (in watts) of each unit produced. The pattern below shows whether each unit's output was above $(A)$ or below $(B)$ the desired specification. Research question: At $\alpha=.05$, do the deviations follow a random pattern? [.] Watts
$B A A B B B A B A B A A B A B B A B B A A B A B A$
AA B BAA AA B BAA BAA AAB BAABAA

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Key Concepts

Hypothesis Testing

Hypothesis testing is a method for making statistical decisions using experimental data. It involves formulating a null hypothesis, which typically represents a default position (such as the process being random), and an alternative hypothesis representing a different scenario. Statistical significance levels, like ? = 0.05, help determine whether there is enough evidence to reject the null hypothesis in favor of the alternative.

Runs Test

The runs test is a nonparametric statistical test used to determine whether a sequence of data points is occurring in a random order. In quality control applications, it examines the order of deviations (such as outcomes above or below a target) to detect non-random patterns, which may suggest that the process is being influenced by special causes.

Control Chart

A control chart is a statistical tool used in quality control and statistical process control (SPC) to monitor and analyze the performance of a process over time. It plots process data against predefined control limits, helping to identify variations that may signify potential problems or improvements in the process.

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