Answer to Question #214159 in Statistics and Probability for Anisha Radhika

Question

Assume you found from the Annual Reports of the Local Police Station found that in a sample of 500 female reports on domestic violence over the 30-day period, 350 were not referred by the Women Crisis Centre. a) Based on the information provided, estimate 95 percent confidence interval for all the females who have been suggested to complain at the Local Police Station by the Crisis Centre. b) Interpret your findings.

Answer 1

(a)

We need to construct the 95% confidence interval for the population proportion. We have been provided with the following:

favorable cases X = 350

sample size N =500

The sample proportion is computed as follows, based on the sample size N =500 and the number of favorable cases X =350:

$p=\frac {X}{N}=\frac {350}{500}=0.7$

The critical value for $\alpha =0.05$ is $z_c=z_(1-\frac {\alpha}{2})=1.96$

The corresponding confidence interval is computed as shown below:

$CI(Proportional)= (p-z_c(\frac {p(1-p)}{n})^\frac{1}{2}, p+ z_c(\frac {p(1-p)}{n})^\frac {1}{2})$

$=(0.7 - 1.96\times(\frac {0.7(1-0.7)}{500})^\frac{1}{2}, 0.7 +1.96\times(\frac {0.7(1-0.7)}{500})^\frac {1}{2})$

$=(0.66,0.74)$

(b)

Based on the data provided, the 95% confidence interval for the population proportion is $0.66<p<0.74$, which indicates that we are 95% confident that the true population proportion, p is contained by the interval (0.66,0.74).