Question

1. a survey of 150 households finds that 45% of respondents recycle regularly. calculate the margin of error (me) at a 95% confidence level (z = 1.96).

a. 7.52%
b. 7.45%
c. 7.96%
d. 7.49%

Explanation:

Step1: Identify the formula for margin of error

The formula for margin of error for a proportion is $ME = Z\sqrt{\frac{p(1 - p)}{n}}$, where $Z$ is the z - score, $p$ is the sample proportion, and $n$ is the sample size.

Step2: Identify the values of $Z$, $p$, and $n$

We are given that $Z = 1.96$ (for 95% confidence level), $p=0.45$ (45% expressed as a decimal), and $n = 150$.

Step3: Substitute the values into the formula

$ME=1.96\sqrt{\frac{0.45\times(1 - 0.45)}{150}}$. First, calculate $1-0.45 = 0.55$. Then $0.45\times0.55=0.2475$. $\frac{0.2475}{150}=0.00165$. $\sqrt{0.00165}\approx0.0406$. Then $1.96\times0.0406\approx0.0796$ or $7.96\%$.

Answer:

C. 7.96%