It is generally known that boys grow at an unusually fast rate between the ages of about 12 and 14.

Following are heights, in inches of 40 boys, measured at age 12 and again at age 14.

a. Construct a 95% confidence interval for the mean increase in height for boys between the ages of 12 and 14.

b. A pediatrician claims that the mean increase in height is 5.5 inches. Does the confidence interval contradict this claim?

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Age 12 Age 14 Age 12 Age 14 57.9 62.9 55.4 61.8 61.1 65.9 58.7 64.2 62.7 67.5 64.3 69.8 67.5 73.7 58.1 63.3 59.2 64.9 63.3 69.6 61.4 67.0 61.2 66.4 60.7 65.5 64.5 69.2 55.9 62.1 55.9 62.0 59.7 65.4 60.4 65.7 56.3 61.5 57.8 62.8 63.0 68.5 68.3 73.6 58.6 63.9 63.0 67.7 61.1 65.8 64.4 69.2 59.5 64.5 58.2 64.6 61.6 66.3 59.7 66.1 59.3 64.2 60.2 65.9 62.1 67.1 63.7 68.3 62.8 68.1 60.2 65.2 65.3 69.9 62.7 67.9 60.4 66.7 55.6 61.7