Question: A 65 year old woman with a low bone density in 1992 was treated with alendronate through the year 1999. Bone density was measured irregularly over this period. The results for change in bone density of the lumbar spine are shown in table 1.

Change in bone density, lumbar spine, over time

Note: \[\sum\limits_{i=1}^{8}{{{t}_{i}}}\] =375, \[\sum\limits_{i=1}^{8}{{{x}_{i}}=6.69}\] , \[\sum\limits_{i=1}^{8}{t_{i}^{2}}\] =25,849, \[\sum\limits_{i=1}^{8}{x_{i}^{2}}\] =5.60197, \[\sum\limits_{i=1}^{8}{{{x}_{i}}{{t}_{i}}}\] =320.874

The normal change in bone density over time from age 40 to age 80 is a decrease of 0.15 gm/ \[c{{m}^{2}}\]. Does the rate of change in this woman differ significantly from the expected age-related change?