Wildlife biologists inspect 157 deer taken by hunters and...

Wildlife biologists inspect 157 deer taken by hunters and find 33 of them carrying ticks that test positive for Lyme disease. a) Create a $90 \%$ confidence interval for the percentage of deer that may carry such ticks. b) If the scientists want to cut the margin of error in half, how many deer must they inspect? c) What concerns do you have about this sample?

Wildlife biologists inspect 157 deer taken by hunters and find 33 of them carrying ticks that test positive for Lyme disease.
a) Create a $90 \%$ confidence interval for the percentage of deer that may carry such ticks.
b) If the scientists want to cut the margin of error in half, how many deer must they inspect?
c) What concerns do you have about this sample?

Key Concepts

Sample Size Determination

Sample size determination involves calculating the number of observations needed to achieve a desired level of precision in an estimate. When the goal is to reduce the margin of error, this calculation shows that the required sample size increases, often quadratically, relative to the desired decrease in the margin of error.

Sampling Bias

Sampling bias occurs when the sample collected is not representative of the overall population, leading to results that may systematically differ from the true values. Concerns about sampling bias include the method of selecting subjects, the timing, and the context under which the sampling occurs, all of which can affect the generalizability of the findings.

Confidence Interval

A confidence interval is a range of values, derived from sample statistics, that is likely to contain the true parameter of a population. In the context of proportions, it estimates the percentage of the population with a particular characteristic, providing an interval within which the true population proportion is expected to lie with a given level of confidence.

Margin of Error

The margin of error quantifies the amount of random sampling error in a survey's results. It represents the maximum expected difference between the true population parameter and a sample estimate, and is influenced by the confidence level, variability in the data, and the sample size.

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