Answer :
Answer:
[tex]\hat{\theta} \pm z_{\frac{\alpha}{2}}(\hat{\sigma_{\theta}})[/tex]
Step-by-step explanation:
We are given the following in the question:
[tex]\hat{\theta}[/tex] is distributed normally.
Mean = [tex]\hat{\theta}[/tex]
Standard error = [tex]\hat{\sigma_{\theta}}[/tex]
Significance level = [tex]\alpha[/tex]
Thus, the confidence percentage is
[tex]100(1 - \alpha)\%[/tex]
Confidence interval:
[tex]\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}[/tex]
[tex]\mu \pm z_{critical}(\text{Standard error})[/tex]
[tex]z_{critical}\text{ at}~\alpha = z_{\frac{\alpha}{2}}[/tex]
Putting the values, we get,
[tex]\hat{\theta} \pm z_{\frac{\alpha}{2}}(\hat{\sigma_{\theta}})[/tex]
which is the required confidence interval.