Questions: Question 2 of 3 (1 point) I Question Attempt 1 of 1 ≡ 1 2 3 Find the critical value tα / 2 needed to construct a confidence interval of the given level with the given sample size. Round the answer to at least three decimal places. Level 98%, sample size 24 . Critical value =

Question 2 of 3 (1 point) I Question Attempt 1 of 1
≡ 1
2
3

Find the critical value tα / 2 needed to construct a confidence interval of the given level with the given sample size. Round the answer to at least three decimal places.

Level 98%, sample size 24 .
Critical value =

Transcript text: Question 2 of 3 (1 point) I Question Attempt 1 of 1 $\equiv 1$ 2 3 Find the critical value $t_{\alpha / 2}$ needed to construct a confidence interval of the given level with the given sample size. Round the answer to at least three decimal places. Level $98 \%$, sample size 24 . Critical value $=$ $\square$

Solution

Solution Steps

Step 1: Calculate Degrees of Freedom

The degrees of freedom (df) is calculated as $n - 1$, where $n$ is the sample size. Here, $df = 24 - 1 = 23$.

Step 2: Determine Alpha Level

The alpha level ($\alpha$) is calculated as $1 - CL$, where $CL$ is the confidence level expressed as a decimal. For a two-tailed test, we consider $\alpha / 2$. Here, $\alpha = 1 - 0.98 = 0.02$, thus $\alpha / 2 = 0.01$.

Step 3: Find the Critical Value

Using a $t$-distribution table or software, we find the critical value $t_{\alpha / 2}$ that corresponds to the degrees of freedom ($df = 23$) and the determined alpha level ($\alpha / 2 = 0.01$). The critical value is approximately 2.5.