Question: Refer to Exercise. Suppose that from that same data set, we want to compute the average difference between the heights of adult British men and adult British women-not the average difference within married couples.
a. Which of the two methods in Exercise would be appropriate for this situation?
b. The 200 men in the sample had a mean height of 68.2 inches, with a standard deviation of 2.7 inches. The 200 women had a mean height of 63.1 inches, with a standard deviation of 2.5 inches. Assuming these were independent samples, compute a 95% confidence interval for the mean difference in heights between British males and females. Interpret the resulting interval in words that a statistically naive reader would understand.
Exercise: 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.