Construct the Indicated Confidence Interval for the Difference Between the Two

question 31

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. $$\begin{array} { | c | c | } \hline \hline \text { Type A } & \text { Type B } \\\hline \bar { x } _ { 1 } = 71.5 \mathrm { hrs } & \bar { x } _ { 2 } = 68.5 \mathrm { hrs } \\\hline \mathrm { s } _ { 1 } = 3.4 \mathrm { hrs } & \mathrm { s } _ { 2 } = 3.6 \mathrm { hrs } \\\hline n _ { 1 } = 11 & n _ { 2 } = 9 \\\hline \hline\end{array}$$ Construct a $99 \%$ confidence interval for $\mu _ { 1 } - \mu _ { 2 }$ , the difference between the mean drying time for paint type A ar the mean drying time for paint type B.

• A) \(- 2.24\) hrs \(< \mu _ { 1 } - \mu _ { 2 } < 8.24 \mathrm { hrs }\)
• B) \(- 1.00\) hrs \(< \mu _ { 1 } - \mu _ { 2 } < 7.00\) hrs
• C) \(- 1.51\) hrs \(< \mu _ { 1 } - \mu _ { 2 } < 7.51\) hrs
• D) \(- 0.14 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 6.14 \mathrm { hrs }\)

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Definitions:

Anti-rH

A type of antibody directed against the Rh factor on red blood cells, significant in blood transfusion and Rh incompatibility in pregnancy.

Platelets

Small, disc-shaped cell fragments in the blood that are crucial for blood clotting and preventing excessive bleeding following injury.

Coagulation

The process of blood changing from a liquid to a gel, forming a blood clot, which is crucial for stopping bleeding.

Heparin

An anticoagulant medication used to prevent and treat blood clots.