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 \(\mathrm { H } _ { \mathrm { a } } : \mu _ { 1 } \leq \mu _ { 2 }\).

---

Definitions:

Cesarean Delivery

A surgical procedure used to deliver a baby through incisions in the abdomen and uterus, often when a vaginal delivery would put the baby or mother at risk.

Fetus

A developing child, from eight weeks after conception until birth.

Heart Rate

The number of heartbeats per unit of time, typically measured in beats per minute (BPM), indicating cardiovascular health and physical condition.

Preterm

Preterm refers to babies born before 37 weeks of gestation, who often face increased risks of health issues and developmental delays compared to full-term infants.