State what the given confidence interval suggests about the two population means.
-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.
$\begin{array}{l|r}
\text { Type } \mathrm{A} & \text { Type } \mathrm{B} \
\hline \mathrm{x}_{1}=77.1 \text { hrs } & \overline{\mathrm{x}}_{2}=63.5 \mathrm{hrs} \
\mathrm{s}_{1}=4.5 \mathrm{hrs} & \mathrm{s}_{2}=5.1 \mathrm{hrs} \
\mathrm{n}_{1}=11 & \mathrm{n}_{2}=9
\end{array}$
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: $7.30$ hrs $

Question

State what the given confidence interval suggests about the two population means.
-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. 
$\begin{array}{l|r}
\text { Type } \mathrm{A} & \text { Type } \mathrm{B} \
\hline \mathrm{x}_{1}=77.1 \text { hrs } & \overline{\mathrm{x}}_{2}=63.5 \mathrm{hrs} \
\mathrm{s}_{1}=4.5 \mathrm{hrs} & \mathrm{s}_{2}=5.1 \mathrm{hrs} \
\mathrm{n}_{1}=11 & \mathrm{n}_{2}=9
\end{array}$
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: $7.30$ hrs $< \mu _ { 1 } - \mu _ { 2 } < 19.90 \mathrm { hrs }$ 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 greater than the mean drying time for paint type B. The modification
Seems 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 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.
D) 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.

Quizplus · Accepted Answer

The confidence interval $7.30$ hrs $< \mu _ { 1 } - \mu _ { 2 } < 19.90 \mathrm { hrs }$ includes only positive values, indicating that the mean drying time for paint type A is greater than for paint type B, suggesting the modification is effective in reducing drying times.

State What the Given Confidence Interval Suggests About the Two