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:

Transportation Workers

Individuals engaged in jobs related to the transport of goods and people, including drivers, pilots, and railroad and ship workers.

Collective Bargaining

The process of negotiation between employers and a group of employees aimed at agreements to regulate working salaries, working conditions, benefits, and other aspects of workers' compensation and rights.

Union Shop

A place of employment where the employer may hire either labor union members or non-members but where non-members must become members within a specified period of time or lose their jobs.

Nonunion Workers

Employees who are not members of a labor union and, as such, typically do not enjoy the collective bargaining rights and benefits that union members do.