Question

find the margin of error for the given values of c, s, and n.
c = 0.90, s = 3.4, n = 8
click the icon to view the t - distribution table.
the margin of error is. (round to three decimal places as needed.)

Explanation:

Step1: Find the degrees of freedom and significance level

Degrees of freedom \(df=n - 1=8 - 1 = 7\).
Significance level \(\alpha=1 - c=1 - 0.90=0.10\), and \(\frac{\alpha}{2}=0.05\).

Step2: Look up the \(t\) - value

From the \(t\) - distribution table, for \(df = 7\) and \(\frac{\alpha}{2}=0.05\), \(t_{\frac{\alpha}{2}}=1.895\).

Step3: Calculate the margin of error formula

The formula for the margin of error \(E=t_{\frac{\alpha}{2}}\frac{s}{\sqrt{n}}\).
Substitute \(t_{\frac{\alpha}{2}} = 1.895\), \(s = 3.4\), and \(n = 8\) into the formula:
\(E=1.895\times\frac{3.4}{\sqrt{8}}\).
First, calculate \(\sqrt{8}\approx2.828\).
Then \(\frac{3.4}{2.828}\approx1.202\).
Finally, \(E=1.895\times1.202\approx2.288\).

Answer:

\(2.288\)