Determine the Null and Alternative Hypotheses for the Proposed Hypothesis $\mu _ { 1 }$

question 55

Multiple Choice

Determine the null and alternative hypotheses for the proposed hypothesis test.
-A company which designs sports shoes has made an improvement to their popular running shoe. They hope that athletes wearing the new running shoe will be able to run faster over short Distances. They will use a paired sample to determine whether the mean time to run 100 meters for Sprinters wearing the new running shoe is less than the mean time to run the 100 meters for
Sprinters wearing the old running shoe.

• A) Let \(\mu _ { 1 }\) denote the mean time to run 100 meters for sprinters wearing the new running shoe and let \(\mu _ { 2 }\) denote the mean time to run 100 meters for sprinters wearing the old running shoe. The null and alternative hypotheses are \(\mathrm { H } _ { 0 } : \mu _ { 1 } > \mu _ { 2 }\) and \(\mathrm { H } _ { \mathrm { a } } : \mu _ { 1 } < \mu _ { 2 }\).
• B) Let \(\mu _ { 1 }\) denote the mean time to run 100 meters for sprinters wearing the new running shoe and let \(\mu _ { 2 }\) denote the mean time to run 100 meters for sprinters wearing the old running shoe. The null and alternative hypotheses are \(\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }\) and \(\mathrm { H } _ { \mathrm { a } } : \mu _ { 1 } < \mu _ { 2 }\).
• C) Let \(\mu _ { 1 }\) denote the mean time to run 100 meters for sprinters wearing the new running shoe and let \(\mu _ { 2 }\) denote the mean time to run 100 meters for sprinters wearing the old running shoe. The null and alternative hypotheses are \(\mathrm { H } _ { 0 } : \mu _ { 1 } < \mu _ { 2 }\) and \(\mathrm { H } _ { \mathrm { a } } : \mu _ { 1 } > \mu _ { 2 }\).
• D) Let \(\mu _ { 1 }\) denote the mean time to run 100 meters for sprinters wearing the new running shoe and let \(\mu _ { 2 }\) denote the mean time to run 100 meters for sprinters wearing the old running shoe. The null and alternative hypotheses are \(\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }\) and \(\mathrm { H } _ { \mathrm { a } } : \mu _ { 1 } \leq \mu _ { 2 }\).

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Definitions:

Active Approach

A management strategy involving ongoing adjustments and proactive measures in portfolio or economic policy decisions to achieve desired outcomes.

Recessionary Gap

A situation where the real GDP is lower than the potential GDP at the full employment level, resulting in underutilized resources and higher unemployment.

Public Policy

A course of action or inaction chosen by public authorities to address a given problem or interrelated set of problems.

Active Policy Approach

A strategy where government policies actively seek to influence economic conditions, such as through fiscal and monetary policies, to achieve specific economic goals.