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In: Statistics and Probability

Blood pressure: A blood pressure measurement consists of two numbers: the systolic pressure, which is the...

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 ( , )
.

Solutions

Expert Solution

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)


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