Question: Using the data presented by Hand and colleagues (1994) and discussed in previous chapters, we would like to estimate the average age difference between husbands and wives in Britain. Recall that the data consisted of a random sample of 200 couples. Following are two methods that were used to construct a confidence interval for the difference in ages. Your job is to figure out which method is correct:

Method 1: Take the difference between the husband's age and the wife's age for each couple, and use the differences to construct a 95% confidence interval for a single mean. The result was an interval from 1.6 to 2.9 years.

Method 2: Use the method presented in this chapter for constructing a confidence interval for the difference in two means for two independent samples. The result was an interval from 0.4 to 4.3 years. Explain which method is correct, and why. Then interpret the confidence interval that resulted from the correct method.