# 8.2.2.1.1 - Example: MLB Age

8.2.2.1.1 - Example: MLB AgeIn a sample of 30 current MLB pitchers, the mean age was 28 years with a standard deviation of 4.4 years. Construct a 95% confidence interval to estimate the mean age of all current MLB pitchers.

This is what we know: \(n=30\), \(\overline{x}=28\), and \(s=4.4\).

In order to compute the confidence interval for \(\mu\) we will need the t multiplier and the standard error (\( \frac{s}{\sqrt{n}}\)).

\(df=n-1=30-1=29\)

For a 95% confidence interval with 29 degrees of freedom, \(t^{*}=2.045\)

\(SE=\dfrac{s}{\sqrt{n}}=\dfrac{4.4}{\sqrt{30}}=0.803\)

Thus, our confidence interval for \(\mu\) is: \(28\pm 2.045(0.803)=28\pm1.643=[26.357,29.643]\)

We are 95% confident that the population mean age is between 26.357 and 29.643.