SCENARIO 18-3
a Quality Control Analyst for a Light Bulb

question 126

Multiple Choice

SCENARIO 18-3
A quality control analyst for a light bulb manufacturer is concerned that the time it takes to produce a
batch of light bulbs is too erratic. Accordingly, the analyst randomly surveys 10 production periods
each day for 14 days and records the sample mean and range for each day. $\begin{array}{ccc} \underline{\text { Day } }& \underline{\bar{X} \text { (in minutes) }} & \underline{\text {R}}\\1 & 58.5 & 5.1 \\2 & 47.6 & 7.8 \\3 & 64.3 & 6.1 \\4 & 60.6 & 5.7 \\5 & 63.7 & 6.2 \\6 & 57.5 & 6.0 \\7 & 55.0 & 5.4 \\8 & 54.9 & 6.1 \\9 & 55.0 & 5.9 \\10 & 62.7 & 5.0 \\11 & 61.9 & 7.1 \\12 & 60.0 & 6.5 \\13 & 58.3 & 5.9 \\14 & 52.0 & 5.2\end{array}$

-Referring to Scenario 18-3, suppose the analyst constructs an R chart to see if the variability in production times is in-control. What is the upper control limit for this R chart?

• A) 10.66
• B) 9.37
• C) 7.98
• D) 6.34

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Definitions:

Sum of Squares

A statistical measure that quantifies the variability or dispersion of a set of numbers by squaring their deviations from the mean.

Coefficient of Determination

A statistical measure represented by R^2, which shows the proportion of variance in the dependent variable that is predictable from the independent variables.

Sum of Squares

A statistical measure that quantifies the variance or dispersion of a set of numbers by summing the squared differences between each number and the mean.

Error SSE

The sum of squared errors (SSE) is a measure used in statistics to quantify the discrepancy between the data and an estimation model.