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murzikaleks [220]
3 years ago
7

Renee wants to estimate the percentage of people who lease a car. She surveys 150 individuals and finds that 33 lease a car. Fin

d the confidence interval for the population proportion with a 90% confidence level.
Mathematics
1 answer:
Oduvanchick [21]3 years ago
5 0

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)

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