Question

Find the confidence level and $\propto$ for

a. $90\%$confidence interval.

b. $94\%$confidence interval.

Short answer

a. $\alpha =0.10$and confidence level is$0.90$

b. $\alpha =0.01$and confidence level is$0.99$

Step-by-step solution

Given Information

We are given with two confidence levels$90\%$and$99\%$.

Calculation of confidence level and α for 90% confidence interval.

We know that

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

$90\%$confidence interval implies $100\times 0.9\%$confidence interval.

$\Rightarrow 1-\alpha =0.90$

Hence, confidence level is $0.90$

$\alpha =1-0.90=0.10$

Calculation of confidence level and α for 99% confidence interval

$99\%$implies $100\times 0.99\%$confidence interval.

$\Rightarrow 1-\alpha =0.99$

Confidence level is $0.99$

and$\alpha =1-0.99=0.01$