Question

In a recent poll, 600 people were asked if they liked dogs, and 43% said they did. Find the margin of error of this poll, at the 95% confidence level.Give your answer to three decimals

Answer 1

Answer:

$0.040$

Explanation:

Here, we want to find the margin of error of the pool

From the question, we have the following:

n = 600

p = 43% = 43/100 = 0.43

q = 1-p = 1-0.43 = 0.57

At 95% confidence level, z = 1.96

We can calculate the margin of error by using the formula below:

$\begin{gathered} MOE\text{ = }\frac{z\sigma}{\sqrt{n}} \\ \\ \sigma\text{ = SD = }\sqrt{pq} \end{gathered}$

Substituting the values, we have it that:

$\begin{gathered} MOE\text{ = }\frac{1.96\times\sqrt{0.43\times0.57}}{\sqrt{600}} \\ \\ MOE\text{ = 0.040} \end{gathered}$