An Inventor Has Developed a New Spray Coating That Is

question 66

Short Answer

An inventor has developed a new spray coating that is designed to improve the wear of bicycle tires. To test the new coating, the inventor randomly selects one of the two tires on each of 50 bicycles to be coated with the new spray. The bicycle is then driven for 100 miles and the amount of the depth of the tread left on the two bicycle tires is measured (in millimeters). It is desired to determine whether the new spray coating improves the wear of the bicycle tires. The data and summary information is shown below: 1 1.452 0.785 $\begin{array}{c|c|c}\text { Bicycle } & \text { Coated Tire }(\mathrm{C}) & \text { Non-Coated Tire (N) } \\\hline 1 & 1.452 & 0.785 \\2 & 1.634 & 0.844 \\\downarrow & \downarrow & \downarrow \\50 & 1.211 & 0.954\end{array}$

$\begin{array} { l l c c } & \text { Coated } & \text { Non-Coated } & \text { Difference } \\ \text { Mean } & 1.38 & 0.85 & 0.53 \\ \text { Std. Dev. } & 0.12 & 0.11 & 0.06 \\ \text { Sample Size } & 50 & 50 & 50 \end{array}$

Use the summary data to construct a $90 \%$ confidence interval for the difference between the means.
A) $0.53 \pm 0.01663$
B) $0.53 \pm 0.04512$
C) $0.53 \pm 0.01396$
D) $0.53 \pm 0.03787$

• A) \(0.53 \pm 0.01663\)
• B) \(0.53 \pm 0.04512\)
• C) \(0.53 \pm 0.01396\)
• D) \(0.53 \pm 0.03787\)

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Definitions:

Nominal Interest Rate

The interest rate which is advertised or stated, without adjustment for the full effects of compounding or inflation.

Semiannual Compounding

The process of applying interest to a principal sum twice a year, leading to interest being earned on interest.

Periodic Interest Rate

The interest rate applied over a specific time period, crucial for calculating interest in savings and loan scenarios.

Present Value

The value today of a future amount of money or sequence of cash payments, calculated using a designated return rate.