State What the Given Confidence Interval Suggests About the Two

question 25

Multiple Choice

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.

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