Q 8.27 - Elementary Statistics

Question

Find the confidence level and $\propto$  for

a. $90\%$confidence interval.

b. $94\%$ confidence interval.

Step-by-Step Solution

Answer

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

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

Step 1: Given Information

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

Step 2: 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 $0.90$

$\alpha =1-0.90=0.10$

Step 3: Calculation of confidence level and &#945; for 99 % confidence interval

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

$\Rightarrow 1-\alpha =0.99$

Confidence level is $0.99$

and $\alpha =1-0.99=0.01$