$$ z_{\alpha / 2} $$ for the $$ 91 \% $$ confidence interval $$ z_{\alpha / 2}=\square imes \square $$

Question

$$ z_{\alpha / 2} $$ for the $$ 91 \% $$ confidence interval $$ z_{\alpha / 2}=\square 	imes \square $$

UpStudy AI · Accepted Answer

1. Since the confidence level is $$91\%$$, we have
   $$
   \alpha = 1 - 0.91 = 0.09.
   $$
2. The value in each tail is
   $$
   \frac{\alpha}{2}=0.045.
   $$
3. To find $$ z_{\alpha/2} $$, we need the critical value with a cumulative probability of
   $$
   1 - \frac{\alpha}{2} = 1 - 0.045 = 0.955.
   $$
4. Looking up the standard normal table (or using a calculator) for $$ P(Z\le z)=0.955 $$ gives approximately
   $$
   z \approx 1.70.
   $$
5. In a confidence interval the margin of error is expressed as
   $$
   \text{Margin of Error} = z_{\alpha/2} \times \text{SE},
   $$
   so in this context we have
   $$
   z_{\alpha/2} = 1.70 \times 1.
   $$

Thus, the blanks are filled as follows:
$$
z_{\alpha/2} = 1.70 \times 1.
$$
$$ z_{\alpha/2} = 1.70 \times 1 $$

\( z_{\alpha / 2} \) for the \( 91 \% \) confidence interval \( z_{\alpha / 2}=\square \times \square \)

Solución de inteligencia artificial de Upstudy

Responder

Solución

Extra Insights

preguntas relacionadas

Latest Statistics Questions