An Inventor Has Developed a New Spray Coating That Is

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 $\begin{array}{c|c|c}\text { Bicycle } & \text { Coated Tire (C) } & \text { Non-Coated Tire }(\mathrm{N}) \\\hline 1 & 1.452 & 0.785 \\2 & 1.634 & 0.844 \\\downarrow & \downarrow & \downarrow \\50 & 1.211 & 0.954\end{array}$

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

Identify the correct null and alternative hypothesis for testing whether the new spray coating improves the mean wear of the bicycle tires (which would restult in a larger amount of tread left on the tire).
A) $H _ { 0 } : \mu _ { \mathrm { d } } = 0$ vs. $\mathrm { H } _ { \mathrm { a } } : \mu _ { \mathrm { d } } < 0$
B) $\mathrm { H } _ { 0 } : \mu _ { \mathrm { d } } = 0$ vs. $\mathrm { H } _ { \mathrm { a } } : \mu _ { \mathrm { d } } > 0$
C) $\mathrm { H } _ { 0 } : \mu _ { \mathrm { d } } = 0$ vs. $\mathrm { H } _ { \mathrm { a } } : \mu _ { \mathrm { d } } \neq 0$