Question

find the margin of error for the given values of c, σ, and n.
c = 0.95, σ = 2.9, n = 100
click the icon to view a table of common critical values.
e = (round to three decimal places as needed.)
table of common critical values
level of confidence (z_c)
90% 1.645
95% 1.96
99% 2.575

Explanation:

Step1: Identify the critical - value

Since $c = 0.95$, from the table of common critical values, $z_{c}=1.96$.

Step2: Recall the formula for margin of error

The formula for the margin of error $E$ when the population standard - deviation $\sigma$ is known is $E = z_{c}\frac{\sigma}{\sqrt{n}}$.

Step3: Substitute the given values

We are given $\sigma = 2.9$, $n = 100$, and $z_{c}=1.96$. First, calculate $\sqrt{n}=\sqrt{100}=10$. Then, $\frac{\sigma}{\sqrt{n}}=\frac{2.9}{10}=0.29$. Finally, $E = 1.96\times0.29$.

Step4: Calculate the margin of error

$E=1.96\times0.29 = 0.5684\approx0.568$.

Answer:

$0.568$