A Paint Manufacturer Made a Modification to a Paint to Speed

question 4

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. $$\begin{array} { | c | c | } \hline \text { Type A } & \text { Type B } \\\hline \bar { x } _ { 1 } = 76.3 \mathrm { hrs } & \bar { x } _ { 2 } = 65.1 \mathrm { hrs } \\\hline s _ { 1 } = 4.5 \mathrm { hrs } & s _ { 2 } = 5.1 \mathrm { hrs } \\\hline n _ { 1 } = 11 & n _ { 2 } = 9 \\\hline\end{array}$$ 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 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.
• 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 greater than the mean drying time for paint type B. The modification seems to be effective in
• Reducing drying times.
• D) 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.

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Definitions:

Overapplied Overhead

This occurs when the allocated manufacturing overhead cost is more than the actual overhead costs incurred, leading to a variance.

Underapplied Overhead

The situation where the allocated overhead costs are less than the actual overhead incurred.

Proration

The method of allocating proportions of expenses or incomes across different departments, products, or periods.

Process Costing

An accounting methodology used for homogenous products, which assigns costs to each production unit based on processes or departments.