State What the Given Confidence Interval Suggests About the Two $$\mu _ { 1 } - \mu _ { 2 }$$

question 63

Multiple Choice

State what the given confidence interval suggests about the two population means.
-A paint manufacturer made a modification to a paint to speed up its drying time. Independent simple random samples of 11 cans of type A (the original paint) and 9 cans of type B (the modified paint) were selected and
Applied to similar surfaces. The drying times, in hours, were recorded. The summary statistics are as follows. The following 98% confidence interval was obtained for $$\mu _ { 1 } - \mu _ { 2 }$$ , the difference between the mean drying time
For paint cans of type A and the mean drying time for paint cans of type B: $$\text { B: } 4.90 \mathrm { hrs } < \mu _ { 1 } - \mu _ { 2 } < 17.50 \mathrm { hrs }$$ What does the confidence interval suggest about the population means?

• A) The confidence interval includes only positive values which suggests that the two population means might be equal. There doesn't appear to be a significant difference between the mean drying time for paint Type A and the mean drying time for paint type B. The modification does not seem to be effective in Reducing drying times.
• B) The confidence interval includes 0 which suggests that the two population means might be equal. There doesn't appear to be a significant difference between the mean drying time for paint type A and the mean Drying time for paint type B. The modification does not seem to be effective in reducing drying times.
• C) The confidence interval includes only positive values which suggests that the mean drying time for paint type A is smaller than the mean drying time for paint type B. The modification does not seem to be Effective in reducing drying times.
• D) The confidence interval includes only positive values which suggests that the mean drying time for paint type A is greater than the mean drying time for paint type B. The modification seems to be effective in Reducing drying times.

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Definitions:

NPV

Net Present Value, a method used in capital budgeting to assess the profitability of an investment or project by calculating the difference between the present value of cash inflows and outflows.

Conventional Capital Budgeting

A process of planning and evaluating large-scale investments and expenditures to optimize a company's capital expenditures and investments.

Forecasting Risk

The potential for a forecast to be inaccurate, which can lead to incorrect business decisions and financial performance assessments.

Sensitivity Analysis

A financial model technique used to determine how different values of an independent variable impact a particular dependent variable under a given set of assumptions.