Question

Find the confidence level and $\alpha$for

a. $85\%$confidence interval.

b. $95\%$confidence interval

Short answer

a. Confidence level is $0.85$and $\alpha =0.15$

b. Confidence level is$0.95$and$\alpha =0.05$.

Step-by-step solution

Given Information

We are given with two confidence intervals$85\%$and$95\%$.

Calculation of confidence level and α for 85% confidence interval

We know that

For $100(1-a)\%$confidence interval, confidence interval is $1-a(0<a<1)$

$85\%$confidence level implies localid="1652458855600" $100\times 0.85\%$confidence interval.

$\Rightarrow 1-\alpha =0.85$

and

$\alpha =1-0.85=0.15$

Calculation of confidence level and α for 95% confidence interval

$95\%$confidence interval implies $100\times 0.95\%$confidence interval.

$\Rightarrow 1-\alpha =0.95$

Hence, confidence interval is $0.95$

and$\alpha =1-0.95=0.05$