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 }

Question

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.

Quizplus · Accepted Answer

The confidence interval $4.90 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 17.50 \mathrm { hrs }$ includes only positive values, indicating that the mean drying time for paint type A is greater than that for paint type B. This suggests that the modification is effective in reducing drying times.

A Paint Manufacturer Made a Modification to a Paint to Speed