Math Problem Statement

The tag and release method was used to estimate the population of wolves in a provincial park. The findings were summarized as 'the population is 217 wolves ± 5%, 19 times out of 20.' If the study is repeated 20 times, how often would the researcher expect the mean number of wolves to be within ±5% of 217?

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: 20×0.95=1920 \times 0.95 = 19
  • 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:

  1. What does a confidence interval mean in statistics?
  2. How is the margin of error (±%) calculated in population estimates?
  3. What is the relationship between confidence level and sample size?
  4. How would the confidence level change if we increased the number of samples in the study?
  5. 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