An Inventor Has Developed a New Spray Coating That Is

question 3

Multiple Choice

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:
$$\begin{array}{l}\begin{array} { c | c | c } \text { Bicycle } & \text { Coated Tire } ( \mathrm { C } ) & \text { Non-Coated Tire (N) } \\\hline 1 & 1.452 & 0.785 \\2 & 1.634 & 0.844 \\\downarrow & \downarrow & \downarrow \\50 & 1.211 & 0.954\end{array}\\\\\begin{array} { l l c c } & \text { Coated } & \text { Non-Coated } & \text { Difference } \\\text { Mean } & 1.38 & 0.85 & 0.53 \\\text { Std. Dev. } & 0.12 & 0.11 & 0.06 \\\text { Sample Size } & 50 & 50 & 50\end{array}\end{array}$$ Identify the correct null and alternative hypothesis for testing whether the new spray coating improves the mean wear of the bicycle tires (which would result in a larger amount of tread left on the tire) .

• A) \(\mathrm { H } _ { 0 } : \mu _ { \mathrm { d } } = 0\) vs. \(\mathrm { H } _ { \mathrm { a } } : \mu _ { \mathrm { d } } < 0\)
• B) \(\mathrm { H } _ { 0 } : \mu _ { \mathrm { d } } = 0\) vs. \(\mathrm { H } _ { \mathrm { a } } : \mu _ { \mathrm { d } } \neq 0\)
• C) \(\mathrm { H } _ { 0 } : \mu _ { \mathrm { d } } = 0\) vs. \(\mathrm { H } _ { \mathrm { a } } : \mu _ { \mathrm { d } } > 0\)

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Definitions:

Price Elasticity

The responsiveness of the quantity demanded or supplied of a good to a change in its price, a key concept in understanding consumer and producer behavior.

Crude Oil

A naturally occurring, unrefined petroleum product composed of hydrocarbon deposits and other organic materials, used as a fuel source.

Price-Elasticity

A measure of how much the quantity demanded of a good responds to a change in the price of that good, expressed as a percentage.

Perfectly Inelastic

A situation where the quantity demanded or supplied does not change in response to a price change.