Question

find the margin of error for the given values of c, s, and n.
c = 0.95, s = 3.6, n = 15
click the icon to view the t - distribution table.
the margin of error is. (round to three decimal places as needed.)

Explanation:

Step1: Determine the degrees of freedom

The degrees of freedom \(df=n - 1\). Given \(n = 15\), so \(df=15-1 = 14\).

Step2: Find the \(t\)-value

For a confidence level \(c = 0.95\), the significance level \(\alpha=1 - c=1 - 0.95 = 0.05\). The critical \(t\)-value \(t_{\alpha/2}\) with \(\alpha/2=0.025\) and \(df = 14\) (from the \(t\)-distribution table) is \(t_{0.025,14}=2.145\).

Step3: Calculate the margin of error formula

The formula for the margin of error \(E\) when the population standard deviation \(\sigma\) is unknown (we use the sample standard deviation \(s\) instead) is \(E=t_{\alpha/2}\frac{s}{\sqrt{n}}\).
Substitute \(t_{\alpha/2}=2.145\), \(s = 3.6\), and \(n = 15\) into the formula:

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Answer:

\(2.005\)