Construct a Confidence Interval For $\mu _ { d }$ The Mean of the Differences D for the Population

question 36

Multiple Choice

Construct a confidence interval for $\mu _ { d }$ the mean of the differences d for the population of paired data. Assume that the population of paired differences is normally distributed. Using the sample paired data below, construct a 90% confidence interval for the population mean of all differences.
$\begin{array} { l | l l l l l } \mathrm { A } & 5.0 & 5.1 & 4.6 & 3.5 & 6.0 \\\hline \mathrm { B } & 4.7 & 3.9 & 4.2 & 4.2 & 3.7\end{array}$

• A) \(0.22 < \mu _ { d } < 7.48\)
• B) \(- 0.37 < \mu _ { d } < 1.77\)
• C) \(- 0.07 < \mu _ { d } < 1.47\)
• D) \(- 0.31 < \mu _ { d } < 1.71\)

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Definitions:

Discount Rate

The interest rate charged by central banks for lending money to commercial banks or the rate used in discounted cash flow analysis to determine the present value of future cash flows.

Project Profitability Index

A financial metric that calculates the ratio between the present value of future cash flows and the initial investment of the project.

Profitability Index

A financial metric that measures the relative profitability of an investment, calculated as the present value of future cash flows divided by the initial investment cost.

Investment Projects

Initiatives undertaken by companies or individuals to allocate capital in ways expected to yield returns or gains over time, such as purchasing new equipment or expanding operations.