Question

A report says that the average amount of time a 10-year-old American child spends playing outdoors per day is between 20.36 and 24.82 minutes. What is the margin of error in this report?

Answer 1

The margin of error in a confidence interval depends on the sample size, the standard deviation of the population (which is not given in the problem), and the level of confidence. Since the standard deviation is not given, we cannot calculate the margin of error exactly. However, we can estimate the margin of error using a standard deviation of 1 (which is a common assumption) and a level of confidence of 95%, which corresponds to a z-score of 1.96.

The formula for the margin of error for a 95% confidence interval is:

Margin of error = z * (standard deviation / sqrt(sample size))

Assuming a standard deviation of 1 and a sample size of 1 (since we are talking about the average time of a single child), we get:

Margin of error = 1.96 * (1 / sqrt(1)) ≈ 1.96

Therefore, we can estimate the margin of error in the report to be around 1.96 minutes. This means that the true average time a 10-year-old American child spends playing outdoors per day is likely to be within 1.96 minutes of the reported average, with a 95% level of confidence.

Explanation: