Solving General Linear Model: Part (C) - 95% CI for Recovery Time

[01jbell]

could nay one help me with part (C) in this question

"an anaesthetist is interested in comparing how quickly parients regain con-sciousness after an operation with two types of anaesthetic. it is thought that the recovery time will be related to the length of the operation so this has been includud as a covariate . the model

Y(ij) = B(o) + B(1)*x(ij) + a(i) + E(ij) , i=1,2 j=1,2...10

where Y(ij) is the recovery time (mins) , x(ij) is the operation time( mins) with the constraint a(1)=0 , a(1) realtes to anaesthetic 1 , a(2) realtes to anaesthetic 2


(a) give the design matrix of thsi general linear model with parameter vector

B= [B(0) , B(1) , a(2) ]


(b) fromt eh date the anaestetist found that

B(mean)= [11.53 , 0.70 , 3.57 ]

var(B)= 4.84 -0,23 -1,34
-0,23 0.02 -0,05
-1.34 -0.05 4.15

estimate the mean recovery time for parients whose operation time is 20 minutes using anaesthetic 1


(c) give a 95% cpnfidence interval for the mean recovery time for patients whose operation time is 20 mins using anaesthetic 1


thanks for any help given its C that i can't seem to do

thank you

 

[lippyka]

Answer: The 95% confidence interval for the mean recovery time for patients whose operation time is 20 mins using anaesthetic 1 can be calculated using the following formula: Mean ± (1.96*Standard Error)Mean = 11.53 + 0.7*20 + 0*3.57 = 25.53 minutes Standard Error = √(4.84 + 0.02 × 400 + 4.15 × 3.57^2) = 7.107 minutes Therefore, the 95% confidence interval for the mean recovery time for patients whose operation time is 20 mins using anaesthetic 1 is: 25.53 ± (1.96 * 7.107) = [16.0, 35.1] minutes