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. $\begin{array} { | l | l | }
\hline{ \text { Type A } } & { \text { Type B } } \
\hline \bar { x } _ { 1 } = 71.5 \mathrm { hrs } & \bar { x } _ { 2 } = 68.5 \mathrm { hrs } \
\hline s _ { 1 } = 3.4 \mathrm { hrs } & s _ { 2 } = 3.6 \mathrm { hrs } \
\hline n _ { 1 } = 11 & n _ { 2 } = 9 \
\hline
\end{array}$

Construct a $99 \%$ confidence interval for $\mu _ { 1 } - \mu _ { 2 }$, the difference between the mean drying time for paint type $\mathrm { A }$ and the mean drying time for paint type $\mathrm { B }$.
A) $- 1.51 \mathrm { hrs }

Question

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. $\begin{array} { | l | l | } 
\hline{ \text { Type A } } & { \text { Type B } } \
\hline \bar { x } _ { 1 } = 71.5 \mathrm { hrs } & \bar { x } _ { 2 } = 68.5 \mathrm { hrs } \
\hline s _ { 1 } = 3.4 \mathrm { hrs } & s _ { 2 } = 3.6 \mathrm { hrs } \
\hline n _ { 1 } = 11 & n _ { 2 } = 9 \
\hline
\end{array}$

Construct a $99 \%$ confidence interval for $\mu _ { 1 } - \mu _ { 2 }$, the difference between the mean drying time for paint type $\mathrm { A }$ and the mean drying time for paint type $\mathrm { B }$.
A) $- 1.51 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 7.51 \mathrm { hrs }$
B) $- 2.24 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 8.24 \mathrm { hrs }$
C) $- 1.00 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 7.00 \mathrm { hrs }$
D) $- 0.14 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 6.14 \mathrm { hrs }$

Quizplus · Accepted Answer

The correct confidence interval is calculated using the pooled variance method due to equal population standard deviations assumption and the formula for the confidence interval of the difference between two means. Given the sample sizes, means, and standard deviations, the calculation involves finding the pooled standard deviation, the standard error of the difference between means, and then using the appropriate t-value for a 99% confidence level with degrees of freedom based on the sample sizes. The result is a confidence interval that suggests the true difference in mean drying times between paint types A and B could reasonably be expected to fall within the range of -1.51 to 7.51 hours.

Construct the Indicated Confidence Interval for the Difference Between the Two