Determine Whether the Samples Are Independent or Dependent Construct a 98% Confidence Interval For

question 189

Multiple Choice

Determine whether the samples are independent or dependent.
-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.
$$\begin{array} { l | l } \quad \text { Type A } & \text { Type B } \\\bar { x } _ { 1 } = 75.7 \mathrm { hrs } & \bar { x } _ { 2 } = 64.3 \mathrm { hrs } \\\mathrm { s } _ { 1 } = 4.5 \mathrm { hrs } & \mathrm { s } _ { 2 } = 5.1 \mathrm { hrs } \\\mathrm { n } _ { 1 } = 11 & \mathrm { n } _ { 2 } = 9\end{array}$$
Construct a 98% confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ the difference between the mean drying time for paint of type A and the mean drying time for paint of type B.

• A) \(6.08 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 16.72 \mathrm { hrs }\)
• 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) \(5.85 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 16.95 \mathrm { hrs }\)

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Definitions:

Stakeholders

The groups of people affected by a firm’s decisions.

Decision Making

The cognitive process of selecting a course of action from among multiple alternatives, often involving judgment, evaluation, and reasoning.

Consequentialism

A general approach to ethical dilemmas which requires that we consider the consequences our actions will have on relevant people.

Rigid Set

In mathematics, a set whose members adhere to strict criteria or definitions, often used in contrast to more flexible or loosely defined collections.