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

Provide a significance test to assess whether the mean bone density has significantly changed over time. Please note a 2-tailed p-value.