A Paint Manufacturer Made a Modification to a Paint to Speed

question 40

Multiple Choice

A paint manufacturer made a modification to a paint to speed up its drying time. Independent simple random samples of 11 cans of type A (the original paint) and 9 cans of type B (the Modified paint) were selected and applied to similar surfaces. The drying times, in hours, were Recorded. The summary statistics are as follows.
$\begin{array}{|l|l|}\hline {\text { Type A }} & {\text { Type B }} \\\hline \bar{x}_{1}=76.3 \mathrm{hrs} & \bar{x}_{2}=65.1 \mathrm{hrs} \\\hline s_{1}=4.5 \mathrm{hrs} & s_{2}=5.1 \mathrm{hrs} \\\hline n_{1}=11 & n_{2}=9 \\\hline\end{array}$
The following $98 \%$ confidence interval was obtained for $\mu _ { 1 } - \mu _ { 2 }$ , the difference between the mean drying time for paint cans of type $A$ and the mean drying time for paint cans of type $B$ :
$4.90 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 17.50 \mathrm { hrs }$
What does the confidence interval suggest about the population means?

• A) The confidence interval includes only positive values which suggests that the two population means might be equal. There doesn't appear to be a significant difference Between the mean drying time for paint type A and the mean drying time for paint type B. The modification does not seem to be effective in reducing drying times.
• B) The confidence interval includes 0 which suggests that the two population means might be equal. There doesn't appear to be a significant difference between the mean drying time for
• Paint type A and the mean drying time for paint type B. The modification does not seem to Be effective in reducing drying times.
• C) The confidence interval includes only positive values which suggests that the mean drying time for paint type A is smaller than the mean drying time for paint type B. The Modification does not seem to be effective in reducing drying times.
• D) The confidence interval includes only positive values which suggests that the mean drying time for paint type A is greater than the mean drying time for paint type B. The Modification seems to be effective in reducing drying times.

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Definitions:

Variation

Differences or discrepancies that occur in data, objects, or processes, which can influence outcomes or performances.

Information Overload

A state of having too much information to make a decision or remain informed about a subject.

Societal Pressure

The influence exerted by society on individuals or organizations to conform to norms, behaviors, or values.

BPI Team

A Business Process Improvement (BPI) Team is a group of individuals tasked with analyzing business processes and making recommendations to improve performance, efficiency, and productivity.