Construct the Indicated Confidence Interval for the Difference Between the Two

question 119

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.

$\begin{array}{l|l}\text { Type A } & \text { Type } \mathrm{B} \\\hline \overline{\mathrm{x}}_{1}=75.7 \mathrm{hrs} & \overline{\mathrm{x}}_{2}=64.0 \mathrm{hrs} \\\mathrm{s}_{1}=4.5 \mathrm{hrs} & \mathrm{s}_{2}=5.1 \mathrm{hrs} \\\mathrm{n}_{1}=11 & \mathrm{n}_{2}=9\end{array}$
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) \(6.38\) hrs \(< \mu _ { 1 } - \mu _ { 2 } < 17.02\) hrs
• B) \(6.08 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 17.32 \mathrm { hrs }\)
• C) \(6.15\) hrs \(< \mu _ { 1 } - \mu _ { 2 } < 17.25 \mathrm { hrs }\)
• D) \(6.22 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 17.18 \mathrm { hrs }\)

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Definitions:

Tradeable Property Rights

Legal rights that allow owners to sell, lease, or otherwise transfer their property or its use to others.

Monopoly

An economic scenario where only one seller exists who offers a distinctive product to the marketplace.

Price Discrimination

A pricing strategy where different prices are charged for the same product or service in different markets or to different consumers.

Elastic Demand

A situation where the quantity demanded of a product is highly responsive to changes in its price.