What sample size should be chosen to find the mean number of...

What sample size should be chosen to find the mean number of absences per month for school children to within ±0.2 at a $95 \%$ confidence level if it is known that the standard deviation is $1.1 ?$ (A) $n \leq \sqrt{\frac{0.2}{1.96 \times 1.1}}$ (B) $n \leq \sqrt{\frac{0.2}{1.96 \times 1.1}}$ (C) $n \leq\left(\frac{1.96 \times 1.1}{0.2}\right)^{2}$ (D) $n \leq \sqrt{\frac{0.2}{1.96 \times 1.1}}$ (E) $n \leq\left(\frac{1.96 \times 1.1}{0.2}\right)^{2}$

What sample size should be chosen to find the mean number of absences per month for school children to within ±0.2 at a
$95 \%$ confidence level if it is known that the standard
deviation is $1.1 ?$
(A) $n \leq \sqrt{\frac{0.2}{1.96 \times 1.1}}$
(B) $n \leq \sqrt{\frac{0.2}{1.96 \times 1.1}}$
(C) $n \leq\left(\frac{1.96 \times 1.1}{0.2}\right)^{2}$
(D) $n \leq \sqrt{\frac{0.2}{1.96 \times 1.1}}$
(E) $n \leq\left(\frac{1.96 \times 1.1}{0.2}\right)^{2}$

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Key Concepts

Sample Size Estimation

Sample size estimation is the process of determining the number of observations or replicates required to achieve a desired level of precision in estimating a population parameter. It involves using the margin of error, standard deviation, and the appropriate z-score to ensure that the estimate is within an acceptable range of the true value.

Z-Score

A z-score is a statistical measure that represents the number of standard deviations a data point is from the mean. In the context of confidence intervals, the z-score corresponding to a desired confidence level, such as 1.96 for 95% confidence, is used to determine the multiplier for the standard error.

Margin of Error

The margin of error represents the maximum expected difference between the true population parameter and the sample estimate. It is influenced by the variability in the data, the confidence level, and the sample size, and it quantifies the precision of the estimate.

Confidence Interval

A confidence interval is a range of values, derived from sample data, that is likely to contain the true population parameter with a specified level of confidence. It provides an estimate of uncertainty and variability in the estimation process.

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