Construct the Indicated Confidence Interval for the Difference Between the Two

question 18

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 $\mathrm { B }$ .

• 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:

Supply Curve

A graphical representation showing the relationship between the price of a good and the quantity of the good that sellers are willing to supply.

Demand Curve

A line on a graph that illustrates the quantity of a product that consumers are willing and able to purchase at various price points.

Public Good

A good that is non-excludable and non-rivalrous, meaning individuals cannot be effectively excluded from its use, and one individual's use does not reduce availability to others.

Asymmetric Information

A situation where one party to a market transaction has much more information about a product or service than the other. The result may be an under- or overallocation of resources.