When the data indicate that the point estimate comes from a nearly normal distribution, we can construct a confidence interval for the difference in two means from the framework built in Chapter 2.6. Here a point estimate, , is associated with a normal model with standard error . Using this information, the general confidence interval formula may be applied in an attempt to capture the true difference in means, in this case using a 95% confidence level:
Based on the samples, we are 95% confident that men ran, on average, between 2.998238 minutes slower and 40.67816 minutes faster than women in the 2013 London Marathon.