Pregunta
COMPLETE Which confidence interval is most likely to contain the population parameter? between 7.3 and 8.7 hours of sleep hetween 7.0 and 9.0 hours of sleep between 7.2 and 8.8 hours of sleep
Ask by Wheeler Harrington. in the United States
Feb 25,2025
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Option 2, between 7.0 and 9.0 hours of sleep, is the most likely to contain the population parameter because it has the widest range.
Solución
To determine which confidence interval is most likely to contain the population parameter, we need to consider the width of the intervals. A wider interval is more likely to contain the population parameter.
Given the options:
1. Between 7.3 and 8.7 hours of sleep
2. Between 7.0 and 9.0 hours of sleep
3. Between 7.2 and 8.8 hours of sleep
The interval with the widest range is option 2, between 7.0 and 9.0 hours of sleep. Therefore, option 2 is the most likely to contain the population parameter.
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The second interval, between 7.0 and 9.0 hours of sleep, is the widest and therefore has the highest likelihood of containing the true population parameter. Wider intervals generally provide more coverage because they encompass a broader range of potential values for the population parameter. On the other hand, while the narrower intervals (7.3 to 8.7 and 7.2 to 8.8) might provide a more precise estimate, they also run the risk of missing the true population value if that value lies outside their bounds. So, in terms of likelihood of inclusion, wider is better!
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