Construct the Indicated Confidence Interval for the Difference Between the Two

question 30

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 $98 \%$ confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ , the difference between the mean drying time for paint of type $\mathrm { A }$ and the mean drying time for paint of type $\mathrm { B }$ .

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

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Definitions:

Metatrait

A higher-order personality trait that reflects a fundamental dimension underpinning multiple related traits.

Stability

The consistency or permanence of a certain state, condition, or trait over time.

Agreeableness

A personality trait characterized by attributes such as being kind, sympathetic, cooperative, warm, and considerate.

Cortisol

A steroid hormone produced by the adrenal glands, often referred to as the "stress hormone," as it is involved in response to stress and anxiety.