Construct the Indicated Confidence Interval for the Difference Between the Two

question 56

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

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) \(- 0.14 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 6.14 \mathrm { hrs }\)

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Definitions:

Fixed Factory Overhead Rate

A predetermined rate used to allocate fixed overhead costs to produced goods based on a consistent basis, such as labor hours or machine hours.

Fixed Factory Overhead Volume Variance

A measure used in cost accounting to determine the difference between the budgeted and actual volume of production, affecting the allocation of fixed overhead costs.

Standard Direct Materials

The predetermined cost and quantity of raw materials expected to be used in the production process, used for budgeting and performance evaluation.

Fixed Factory Overhead Volume Variance

The difference between the budgeted and actual fixed overhead costs, due to variations in production levels.