24.1k views
2 votes
A random sample of 400 items from a population shows that 160 of the sample items possess a given characteristic. A random sample of 400 items from a second population resulted in 110 of the sample items possessing the characteristic. Using this data, a 99% confidence interval is constructed to estimate the difference in population proportions which possess the given characteristic. The resulting confidence interval is _______.

User Clark
by
8.8k points

1 Answer

0 votes

Answer:
(0.04,\ 0.21)

Explanation:

The confidence interval for population proportion is given by :-


p_1-p_2\pm z_(\alpha/2)\sqrt{(p_1(1-p_1))/(n_1)+(p_2(1-p_2))/(n_2)}

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

Critical value :
z_(\alpha/2)=2.576


n_1=400 ;\ p_1=(160)/(400)=0.4


n_2=400 ;\ p_2=(110)/(400)=0.275

Then a 99% confidence interval is constructed to estimate the difference in population proportions which possess the given characteristic will be :-


0.4-0.275\pm (2.576)\sqrt{(0.4(1-0.4))/(400)+(0.275(1-0.275))/(400)}\\\\\approx0.125\pm0.085=(0.125-0.085,0.125+0.085)=(0.04,\ 0.21)

Hence, the resulting confidence interval is
(0.04,\ 0.21) .

User Zombaya
by
8.3k points

No related questions found

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