Find the margin of error for the given values of , and n .

The margin of error is . (Round to three decimal places as needed.)
Con to view the t-distribution table.

Ask by Todd Wagner. in the United States

Mar 26,2025

Question

Find the margin of error for the given values of , and n .

The margin of error is . (Round to three decimal places as needed.)
Con to view the t-distribution table.

Ask by Todd Wagner. in the United States

Mar 26,2025

UpStudy AI · Accepted Answer

1. Identify the degrees of freedom:
   $$
   \text{df} = n - 1 = 12 - 1 = 11.
   $$

2. For a confidence level of $$ c = 0.98 $$, the significance level is:
   $$
   \alpha = 1 - c = 0.02,
   $$
   and the critical value corresponds to:
   $$
   \alpha/2 = 0.01.
   $$

3. From the t-distribution table, the critical $$ t $$-value for $$ \alpha/2 = 0.01 $$ and $$ \text{df} = 11 $$ is approximately:
   $$
   t_{0.01, 11} \approx 2.718.
   $$

4. The margin of error is computed using the formula:
   $$
   \text{Margin of Error} = t_{\alpha/2,\,n-1} \left(\frac{s}{\sqrt{n}}\right).
   $$

5. Substitute the given values into the formula:
   $$
   \text{Margin of Error} = 2.718 \left(\frac{3.9}{\sqrt{12}}\right).
   $$

6. Compute the denominator:
   $$
   \sqrt{12} \approx 3.464.
   $$
   Then,
   $$
   \frac{3.9}{3.464} \approx 1.125.
   $$

7. Finally, multiply to obtain the margin of error:
   $$
   2.718 \times 1.125 \approx 3.058.
   $$

Thus, the margin of error is approximately $$ \boxed{3.058} $$.
The margin of error is approximately 3.058.

Find the margin of error for the given values of , and n .

The margin of error is . (Round to three decimal places as needed.)
Con to view the t-distribution table.

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Find the margin of error for the given values of , and n . The margin of error is . (Round to three decimal places as needed.) Con to view the t-distribution table.

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Find the margin of error for the given values of , and n .

The margin of error is . (Round to three decimal places as needed.)
Con to view the t-distribution table.