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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Definitions:

Self-Serving Bias

The tendency to attribute positive outcomes to one's own actions and negative outcomes to external factors.

Attribution Process

The mental operation individuals go through to explain the causes of behavior and events, including their own and others'.

Grades

Levels or steps within a hierarchical evaluation system, typically used to assess performance, quality, or rank.

Attributional Errors

Cognitive biases that occur when one incorrectly attributes the cause of a behavior or event to the wrong source, often leading to misunderstandings.