Math Problem Statement
Solution
Let's break this down and solve the problem:
The question states:
- The population is estimated as 217 wolves ± 5%.
- The study gives these findings 19 times out of 20.
This indicates a 95% confidence level because 19/20 = 0.95, meaning the study's results will fall within the stated range (±5% of 217) 95% of the time.
The question asks: If the study is repeated 20 times, how often would the mean number of wolves be within ±5% of 217?
Solution:
- A 95% confidence level means the range will be correct 95% of the time in repeated trials.
- If the study is repeated 20 times, the expected number of times the result falls within the range is:
- Therefore, the correct answer is:
A) In at least 95% of the studies.
Would you like a deeper explanation or help with related concepts?
Related Questions:
- What does a confidence interval mean in statistics?
- How is the margin of error (±%) calculated in population estimates?
- What is the relationship between confidence level and sample size?
- How would the confidence level change if we increased the number of samples in the study?
- What statistical methods are used to calculate confidence intervals?
Tip:
The confidence interval doesn't guarantee exact results in every trial, but it provides a probability-based estimate of where the true value lies over repeated experiments.
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Math Problem Analysis
Mathematical Concepts
Statistics
Confidence Interval
Probability
Formulas
Confidence Level = (Number of Successes) / (Total Trials)
Expected Occurrences = Total Trials × Confidence Level
Theorems
Confidence Interval Interpretation
Suitable Grade Level
Grades 10-12
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