The 95 % confidence interval for $\beta _ { 0 }$ is the interval
A) $\left( \beta _ { 0 } - 1.96 S E \left( \beta _ { 0 } \right) , \beta _ { 0 } + 1.96 S E \left( \beta _ { 0 } \right) \right)$
B) $\left( \widehat { \beta } _ { 0 } - 1.645 \operatorname { SE } \left( \widehat { \beta } _ { 0 } \right) , \widehat { \beta } _ { 0 } + 1.645 \operatorname { SE } \left( \widehat { \beta } _ { 0 } \right) \right)$
C) $\left( \widehat { \beta } _ { 0 } - 1.96 \operatorname { SE } \left( \widehat { \beta } _ { 0 } \right) , \widehat { \beta } _ { 0 } + 1.96 \operatorname { SE } \left( \widehat { \beta } _ { 0 } \right) \right)$
D) $\left( \widehat { \beta } _ { 0 } - 1.96 , \widehat { \beta } _ { 0 } + 1.96 \right)$

Question

The  95 %  confidence interval for $\beta _ { 0 }$  is the interval
A) $\left( \beta _ { 0 } - 1.96 S E \left( \beta _ { 0 } \right) , \beta _ { 0 } + 1.96 S E \left( \beta _ { 0 } \right) \right)$
B) $\left( \widehat { \beta } _ { 0 } - 1.645 \operatorname { SE } \left( \widehat { \beta } _ { 0 } \right) , \widehat { \beta } _ { 0 } + 1.645 \operatorname { SE } \left( \widehat { \beta } _ { 0 } \right) \right)$
C) $\left( \widehat { \beta } _ { 0 } - 1.96 \operatorname { SE } \left( \widehat { \beta } _ { 0 } \right) , \widehat { \beta } _ { 0 } + 1.96 \operatorname { SE } \left( \widehat { \beta } _ { 0 } \right) \right)$
D) $\left( \widehat { \beta } _ { 0 } - 1.96 , \widehat { \beta } _ { 0 } + 1.96 \right)$

Quizplus · Accepted Answer

The 95% confidence interval for a parameter estimate $\widehat{\beta}_0$ is given by $\left( \widehat{\beta}_0 - 1.96 \times \text{SE}(\widehat{\beta}_0), \widehat{\beta}_0 + 1.96 \times \text{SE}(\widehat{\beta}_0) \right)$, where 1.96 is the critical value for a 95% confidence level from the standard normal distribution.

The 95 % Confidence Interval For β0\beta _ { 0 }β0​

The 95 % Confidence Interval For $\beta _ { 0 }$