Question

1. a random sample of 150 adults finds that 72% favor a new policy. calculate the standard error (se) for this proportion.

a. 0.034
b. 0.037
c. 0.039
d. 0.030

Explanation:

Step1: Identify the formula

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

Step2: Convert percentage to decimal

Given $p = 72\%=0.72$ and $n = 150$.

Step3: Calculate $(1 - p)$

$1 - p=1 - 0.72 = 0.28$.

Step4: Calculate $p(1 - p)$

$p(1 - p)=0.72\times0.28 = 0.2016$.

Step5: Calculate $\frac{p(1 - p)}{n}$

$\frac{p(1 - p)}{n}=\frac{0.2016}{150}=0.001344$.

Step6: Calculate the standard - error

$SE=\sqrt{0.001344}\approx0.037$.

Answer:

B. 0.037