Question

Renee wants to estimate the percentage of people who lease a car. She surveys 150 individuals and finds that 33 lease a car. Find the confidence interval for the population proportion with a 90% confidence level.

Answer 1

Answer: $(0.164,\ 0.276)$

Step-by-step explanation:

The confidence interval of population proportion is given by :-

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

Given : Sample size : $n=150$

The proportion of individuals lease a car :$hat{p}=\dfrac{33}{150}=0.22$

Significance level : $\alpha: 1-0.9=0.1$

Critical value : $z_{\alpha/2}=1.645$

Then, the confidence interval of population proportion is given by :-

$0.22\pm (1.645)\sqrt{\dfrac{0.22(1-0.22)}{150}}\\\\\approx0.22\pm0.056=(0.164,\ 0.276)$

Hence, the confidence interval for the population proportion with a 90% confidence level= $(0.164,\ 0.276)$