Step 1 :Given the pulse rates of 11 sets of twins, we first calculate the differences between each pair of twins' pulse rates. The differences are: 1, 12, -5, 7, -17, 4, -2, 12, 0, -3, 4.
Step 2 :Next, we calculate the mean of these differences, which is approximately \(1.18\).
Step 3 :We also calculate the standard deviation of these differences, which is approximately \(8.26\).
Step 4 :Given that the number of pairs of twins is 11, the degrees of freedom is \(11 - 1 = 10\).
Step 5 :Given a confidence level of 98%, the alpha level is \(1 - 0.98 = 0.02\).
Step 6 :Using a t-distribution table or calculator, we find the critical t-value for a two-tailed test with 10 degrees of freedom and an alpha level of 0.02 to be approximately \(2.76\).
Step 7 :We then calculate the margin of error by multiplying the critical t-value by the standard deviation and dividing by the square root of the number of pairs of twins. The margin of error is approximately \(6.88\).
Step 8 :Finally, we calculate the confidence interval by subtracting and adding the margin of error from the mean difference. The 98% confidence interval for the difference of the average pulse rates of twins is \(\boxed{(-5.7, 8.1)}\) beats per minute.