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

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 and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

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

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

So the sample proportion is

Standard error

So the correct answer is:

B. 0.3 and 0.022

step-by-step explanation:

graph using a few selected

x         y

-1       15

0         6

1         2.4

2       0.96