Answer:
For this case we know that the confidence level is 90% so then the significance level is [tex]\alpha=1-0.9 =0.1[/tex] and [tex]\alpha/2 =0.05[/tex]. And we can find in the normal standard distribution a value who accumulates 0.5 of the area on each tail and we got:
[tex] z_{\alpha/2}= \pm 1.645[/tex]
And the best option would be:
1.645
Step-by-step explanation:
We assume that the parameter of interest is [tex]\theta[/tex] and we can assume that the distribution for this parameter is normally distributed so then the confidence interval assuming a two sided interval is given by:
[tex]\hat \theta \pm z_{\alpha/2} SE[/tex]
Where [tex]\hat \theta[/tex] represent the estimator for the parameter, SE the standard error and [tex]z_{\alpha/2}[/tex] the critical value.
For this case we know that the confidence level is 90% so then the significance level is [tex]\alpha=1-0.9 =0.1[/tex] and [tex]\alpha/2 =0.05[/tex]. And we can find in the normal standard distribution a value who accumulates 0.5 of the area on each tail and we got:
[tex] z_{\alpha/2}= \pm 1.645[/tex]
And the best option would be:
1.645
