Question

You have collected data for the 50 U.S. states and estimated the following relationship between the change in the unemployment rate from the previous year and the growth rate of the respective state real GDP ​(​). The results are as​ follows: ​

Δur= (0.12) -(0.04)x gy, R2= 0.36, SER= 0.78

Assuming that the estimator has a normal​ distribution, the​ 95% confidence interval for the slope is approximately the​ interval:

a. [-0.31, 0.15]
b. [2.57, 3.05 ]
c. [-0.33, - 0.13]
d. [-0.13, -0.15]

Answer 1

[ -0.13, -0.15 ] ( D )

Step-by-step explanation:

Given data :

sample size ( n ) = 50

Independent variable ( p ) = 1

determine the confidence interval for the slope

Df ( degree of freedom ) = n - p - 1 = ( 50 - 1 - 1 ) = 48

b ( estimated slope ) = -0.23

Standard error of slope = 0.04

confidence interval = 95%

For confidence interval of 95% and Df of 48 ; critical value ( t ) = 2.011

∴ Confidence interval

= -0.23 ± ( 2.011 * 0.04)

= -0.23 ± 0.08044

= [ -0.13, -0.15 ]