Question

A Bernoulli random variable X has unknown success probability p. Using 100 independent samples of X, find a confidence interval estimate of p with confidence coefficient 0.99. If ????????100 = 0.06, what is our interval estimate

Answer 1

Answer: $(0.0445,\ 0.0755)$

Step-by-step explanation:

The confidence interval for the population proportion is given by :-

$p\pm z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}$

Given : A Bernoulli random variable X has unknown success probability p.

Sample size : $n=100$

Unknown success probability : $p=0.06$

Significance level : $\alpha=1-0.99=0.01$

Critical value : $z_{\alpha/2}=2.576$

Now, the 99% confidence interval for true proportion will be :-

$0.06\pm(2.576)\sqrt{\dfrac{0.06(0.06)}{100}}\\\\\approx0.06\pm(0.0155)\\\\=(0.06-0.0155,\ 0.06+0.0155)\\\\=(0.0445,\ 0.0755)$

Hence, the 99% confidence interval for true proportion= $(0.0445,\ 0.0755)$