134k views
1 vote
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

n = 130
x = 69; 90% confidence

a. 0.463 < p < 0.599
b. 0.458 < p < 0.604
c. 0.461 < p < 0.601
d. 0.459 < p < 0.603

User Brennan
by
7.8k points

1 Answer

0 votes

Answer:

d. 0.459 < p < 0.603

Explanation:

We have to calculate a 90% confidence interval for the proportion.

The sample proportion is p=0.531.


p=X/n=69/130=0.531

The standard error of the proportion is:


\sigma_p=\sqrt{(p(1-p))/(n)}=\sqrt{(0.531*0.469)/(130)}\\\\\\ \sigma_p=√(0.001916)=0.044

The critical z-value for a 90% confidence interval is z=1.645.

The margin of error (MOE) can be calculated as:


MOE=z\cdot \sigma_p=1.645 \cdot 0.044=0.072

Then, the lower and upper bounds of the confidence interval are:


LL=p-z \cdot \sigma_p = 0.531-0.072=0.459\\\\UL=p+z \cdot \sigma_p = 0.531+0.072=0.603

The 90% confidence interval for the population proportion is (0.459, 0.603).

User JDiMatteo
by
8.1k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories