Find the critical val. ($t_{\alpha \text{⁄}2}$) for each confidence interval.
(A) Confidence Level = $95\%,n=35$

• A. 2.73
• B. 2.44
• C. 1.69
• D. 2.03

Answer: (D)

Verified step by step guidance

1. Step 1: Understand the problem. We are tasked with finding the critical value (t_{α⁄2}) for a given confidence level and sample size. The confidence level is 95%, and the sample size (n) is 35. The critical value is used in constructing confidence intervals for the population mean when the population standard deviation is unknown.
2. Step 2: Determine the degrees of freedom (df). The degrees of freedom for a t-distribution is calculated as df = n - 1, where n is the sample size. For this problem, df = 35 - 1.
3. Step 3: Identify the significance level (α). The confidence level is 95%, so the significance level is α = 1 - 0.95 = 0.05. Since we are looking for t_{α⁄2}, divide α by 2 to get α⁄2 = 0.05⁄2 = 0.025.
4. Step 4: Use a t-distribution table or statistical software to find the critical value t_{α⁄2}. Look up the value corresponding to α⁄2 = 0.025 and df = 34 in the t-distribution table. Alternatively, use statistical software to compute the value.
5. Step 5: Verify the critical value. Compare the obtained t_{α⁄2} value with the provided options (2.73, 2.44, 1.69, 2.03) to ensure it matches the correct answer.