The table below gives the statistics related to crime on cam

The table below gives the statistics related to crime on campus. X represents student enrollment (in thousands) and y represents the number of burglaries in a year on campus.

Find a Se.

Find a 95% confidence interval for the number of burglaries at a college with an enrollment of 22,000 students.

Solution

Using technology, the standard error for the y estimate is (in Excel, you can use the LINEST function):

sey = 13.05899922

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Using technology, the equation of the regression line is

y^ = 1.826127168x -4.129028902

Thus, if x = 22000,

y^ = 36518.41432

Here, we have

df = n - 2 = 6

Note that              
              
Lower Bound = X - t(alpha/2) * se              
Upper Bound = X + t(alpha/2) * se              
              
where              
              
df =    6          
X = sample mean =    36518.41432          
t(alpha/2) = critical z for the confidence interval =    2.570581836          
se = standard error =    13.05899922          
              
Thus,              
              
Lower bound =    36484.84509          
Upper bound =    36551.98355          
              
Thus, the confidence interval is              
              
(   36484.84509   ,   36551.98355   ) [ANSWER]