Q 8.28 - Elementary Statistics

Question

Find the confidence level and $\alpha$ for

a. $85\%$confidence interval.

b.  $95\%$confidence interval

Step-by-Step Solution

Answer

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

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

Step 1: Given Information

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

Step 2: 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 $100\times 0.85\%$confidence interval.

$\Rightarrow 1-\alpha =0.85$

and

$\alpha =1-0.85=0.15$

Step 3: Calculation of confidence level and &#945; 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 $\alpha =1-0.95=0.05$