Question

Construct both a 9090% and a 9595% confidence interval for β1β1.
β^1=38, s=6.4, SSxx=45, n=10β^1=38, s=6.4, SSxx=45, n=10
90% :  ≤β1≤≤β1≤
95% :  ≤β1≤≤β1≤

Note: You can earn partial credit on this problem.

Answer 1

for 90% CI:

sample size n=				10
number of independent variables p=				1
degree of freedom =n-p-1=				8
estimated slope b=				38
standard error of slope=sb= s/sqrt(SSx)=						0.954056
for 90 % confidence and 8degree of freedom critical t=						1.8600
90% confidence interval =b1 -/+ t*standard error=					(36.2255,39.7745)

for 95% CI:

for 95 % confidence and 8degree of freedom critical t=						2.3060
95% confidence interval =b1 -/+ t*standard error=					(35.7999,40.2001)