A random sample of 100 people was selected from a population of customers at a local bank. The mean age of these customers was 40. If the population standard deviation is thought to be 5 years, the margin of error for a 95 percent confidence interval estimate is .98 year.

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Quizplus · Accepted Answer

The margin of error for a 95% confidence interval can be calculated using the formula $ME = Z \times \frac{\sigma}{\sqrt{n}}$, where $Z$ is the Z-score corresponding to the confidence level (approximately 1.96 for 95%), $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values: $ME = 1.96 \times \frac{5}{\sqrt{100}} = 1.96 \times 0.5 = 0.98$ year, which matches the statement.

A Random Sample of 100 People Was Selected from a Population