Final answer:
The null hypothesis (H0) states that there is no effect or no difference, typically implying the proportion of interest is equal to a historical or claimed value. The alternative hypothesis (Ha) suggests the opposite, indicating that the proportion is different from the historical or claimed value. The exact hypotheses cannot be stated without additional information, such as a historical or claimed proportion.
Step-by-step explanation:
The null and alternative hypotheses are statements that reflect the possible outcomes for a hypothesis test concerning some statistical characteristic of the population. In the case of Jose's random sample of 138 people and their heart rates after running a mile, the null hypothesis (H0) typically states there is no effect or no difference, implying that the true proportion of people with a heart rate of more than 120 bpm is equal to some historical or claimed value. The alternative hypothesis (Ha) suggests there is an effect or a difference, indicating that the true proportion of people with heart rates over 120 bpm is not equal to the historical or claimed value.
For instance, if it was historically claimed that 50% of people between the ages of 18 and 25 have a heart rate over 120 bpm after running a mile, the hypotheses would be formulated as:
- Null hypothesis (H0): p = 0.5 (The proportion is equal to 50%)
- Alternative hypothesis (Ha): p ≠ 0.5 (The proportion is not equal to 50%)
In this specific case, since the historical or claimed value is not mentioned, it's not possible to provide the exact hypotheses without additional information. If Jose is specifically interested in whether the proportion exceeds 50%, the alternative hypothesis might state that the true proportion is greater than 50%, and the null hypothesis would state that it is at most 50%.