Question

A simple random sample of 450 residents in the state of New York is taken to estimate the proportion of people who live within one mile of a hazardous waste site. If 135 of the residents in the sample live within one mile of a hazardous waste site, what are the values of the sample proportion of people who live within one mile of a hazardous waste site and its standard error?
A. 0.3 and 0.01
B. 0.3 and 0.022
C. 0.3 and 0.21
D. 0.7 and 0.022

Answer 1

Answer:

B. 0.3 and 0.022

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a sample proportion p in a sample of size n, the standard error is $s = \sqrt{\frac{p(1-p)}{n}}$

135 of the 450 residents sampled live within one mile of a hazardous waste site.

So the sample proportion is $p = \frac{135}{450} = 0.3$

Standard error

$s = \sqrt{\frac{0.3*0.7}{450}} = 0.022$

So the correct answer is:

B. 0.3 and 0.022