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.

Can you conclude that the mean increase in height is greater than 5 inches?

a. State the null and alternate hypotheses.

b. Compute the test statistic.

c. State a conclusion. Use the α = 0.05 level of significance.

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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