Question

Blood pressure: A blood pressure measurement consists of two numbers: the systolic pressure, which is the maximum pressure taken when the heart is contracting, and the diastolic pressure, which is the minimum pressure taken at the beginning of the heartbeat. Blood pressures were measured, in millimeters, for a sample of 7 adults. The following table presents the results. The least-squares regression line =y=+b0b1x+24.83840.4499x, =se7.161065, =Σ−xx2407.43, and x=120.71 are known for this data.

Systolic	Diastolic
112	75
118	88
130	76
123	77
116	70
133	91
113	77

1.)Construct a 90% prediction interval for the diastolic pressure of a particular person whose systolic pressure is 120. Round your answer to at least three decimal places.

A 90%prediction interval for the diastolic pressure of a particular person whose systolic pressure is 120 is ( , ) .

Answer 1

X Value=   120                      
Confidence Level=   90%                      
                          
                          
Sample Size , n=   7                      
Degrees of Freedom,df=n-2 =   5                      
critical t Value=tα/2 =   2.015   [excel function: =t.inv.2t(α/2,df) ]                  
                          
X̅ =    120.71                      
Σ(x-x̅)² =Sxx   407                      
Standard Error of the Estimate,Se=   7.1611                      
                          
Predicted Y at X=   120   is                  
Ŷ =   24.8384   +   0.4499   *   120   =   78.822

For Individual Response Y                  
standard error, S(ŷ)=Se*√(1+1/n+(X-X̅)²/Sxx) =   7.6597              
margin of error,E=t*std error=t*S(ŷ)=    2.0150   *   7.66   =   15.4347
                  
Prediction Interval Lower Limit=Ŷ -E =   78.822   -   15.43   =   63.387
Prediction Interval Upper Limit=Ŷ +E =   78.822   +   15.43   =   94.256

A 90%prediction interval for the diastolic pressure of a particular person whose systolic pressure is 120 is (63.387 , 94.256)