What is the typical age of a person who renews his or her...

What is the typical age of a person who renews his or her driver's license online? From a random sample of 460 driver's license renewal transactions, the mean age was 42.6 and the standard deviation was 5.4. Compute the $98 \%$ confidence interval estimate of the mean age of online renewal users in this county.

Key Concepts

Standard Error

The standard error measures the variability of the sample mean from the true population mean. It is calculated by dividing the sample standard deviation by the square root of the sample size, and it reflects the precision of the sample mean as an estimator.

Central Limit Theorem

The Central Limit Theorem states that, given a sufficiently large sample size, the sampling distribution of the sample mean will be approximately normally distributed regardless of the population’s distribution. This theorem justifies the use of normal-based confidence intervals for estimating the mean.

Margin of Error

The margin of error is the product of the critical value and the standard error. It represents the maximum expected difference between the sample mean and the population mean within the specified confidence level, defining how wide the confidence interval is.

Confidence Interval

A confidence interval is a range of values, derived from sample data, that is likely to contain the true population parameter. It provides an estimate of the uncertainty around the sample statistic and is defined by a confidence level, such as 98%, which indicates the probability that the interval contains the true mean.

Critical Value

The critical value is a point on the distribution, such as the z-score in a normal distribution, that corresponds to the desired level of confidence. It determines how far from the sample mean the interval will extend, allowing the construction of the confidence interval.

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