find the margin of error for the given values of c, s, and n.\nc = 0.90, s = 3.4, n = 8\nclick the icon to…

Explanation:

Step1: Find the degrees of freedom

The degrees of freedom (df=n - 1). Given (n = 8), so (df=8-1 = 7).

Step2: Find the (t)-value

For a confidence level (c = 0.90), the significance level (\alpha=1 - c=1 - 0.90 = 0.10). And (\frac{\alpha}{2}=\frac{0.10}{2}=0.05). Looking up the (t)-distribution table with (df = 7) and (\frac{\alpha}{2}=0.05), we get (t_{\frac{\alpha}{2}}=1.895).

Step3: Calculate the margin of error

The formula for the margin of error (E) (when the population standard deviation (\sigma) is unknown) is (E=t_{\frac{\alpha}{2}}\frac{s}{\sqrt{n}}). Given (s = 3.4), (n = 8), and (t_{\frac{\alpha}{2}}=1.895). First, calculate (\sqrt{n}=\sqrt{8}\approx2.828). Then (E = 1.895\times\frac{3.4}{2.828}). (\frac{3.4}{2.828}\approx1.202). (E=1.895\times1.202\approx2.288).

Answer:

(2.288)