Construct the Indicated Confidence Interval for the Difference Between the Two

question 46

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. Also assume that the population standard deviations are equal ( $\left( \sigma _ { 1 } = \sigma _ { 2 } \right)$ , so that the standard error of the difference between means is obtained by pooling the sample variances .
-A paint manufacturer wanted 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.
$$\begin{array} { r | r } \text { Type A } & \text { Type B } \\\hline \overline { \mathrm { x } } _ { 1 } = 70.7 \mathrm { hr } & \overline { \mathrm { x } } _ { 2 } = 68.6 \mathrm { hr } \\\mathrm { s } _ { 1 } = 3.8 \mathrm { hr } & \mathrm { s } _ { 2 } = 3.6 \mathrm { hr } \\\mathrm { n } _ { 1 } = 11 & \mathrm { n } _ { 2 } = 9\end{array}$$
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) \(- 1.24\) hrs \(< \mu _ { 1 } - \mu _ { 2 } < 5.44\) hours
• B) \(- 2.16\) hrs \(< \mu _ { 1 } - \mu _ { 2 } < 6.36\) hrs
• C) \(- 2.70 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 6.90 \mathrm { hrs }\)
• D) \(- 3.47 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 7.67 \mathrm { hrs }\)

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Definitions:

Coase Theorem

An economic theory proposing that under conditions of no transaction costs, parties can negotiate and arrive at efficient resource allocation and solution to externalities regardless of initial property rights allocation.

Number Of People

A quantitative measure of the people involved or affected in a particular context.

Positive Externalities

Benefits that are enjoyed by a third-party or society as a result of an economic transaction.

Producing Firm

An entity or company involved in the creation of goods or services to be offered to consumers.