Construct the Indicated Confidence Interval for the Difference Between the Two

question 14

Multiple Choice

Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. A paint manufacturer wished to compare the drying times of two different types of paint .Independent simple random samples of 11 cans of type A and 9 cans of type B were selected and applied to similar surfaces. The drying times, in hours, were recorded. The summary statistics are as follows.
$\begin{array}{|l|l|}\hline {\text { Type A }} & {\text { Type B }} \\\hline \bar{x}_{1}=75.7 \mathrm{hrs} & \bar{x}_{2}=64.3 \mathrm{hrs} \\\hline s_{1}=4.5 \mathrm{hrs} & s_{2}=5.1 \mathrm{hrs} \\\hline n_{1}=11 & n_{2}=9 \\\hline\end{array}$

Construct a $99 \%$ confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ , the difference between the mean drying time for paint type A and the mean drying time for paint type B.

• A) \(5.85 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 16.95 \mathrm { hrs }\)
• B) \(5.78 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 17.02 \mathrm { hrs }\)
• C) \(5.92 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 16.88 \mathrm { hrs }\)
• D) \(6.08 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 16.72 \mathrm { hrs }\)

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Definitions:

Generalized Intelligence

A theory proposing that intelligence is a single, general ability that influences performance across a variety of tasks and situations.

Spearman

A psychologist known for his work in intelligence, introducing the theory of general intelligence, or "g" factor, which posits a single underlying intelligence factor that influences cognitive abilities.

Bodily Kinesthetic

A learning style or intelligence that emphasizes physical movement and the awareness and control of bodily motions.

Intrapersonal

Relating to or within a person's own self, often used in context of internal thoughts, feelings, and communication.