Find the critical val. ($t_{\alpha \text{⁄}2}$) for each confidence interval.
(B) Confidence Level = $90\%,n=48$

• A. 2.41
• B. 2.68
• C. 1.68
• D. 1.30

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the problem. We are tasked with finding the critical value (t_{α/2}) for a 90% confidence level with a sample size of n = 48. The critical value is used in constructing confidence intervals and depends on the confidence level and degrees of freedom.
2. Step 2: Calculate the degrees of freedom (df). For a t-distribution, the degrees of freedom are given by df = n - 1, where n is the sample size. In this case, df = 48 - 1.
3. Step 3: Determine the value of α. The confidence level is 90%, so α = 1 - 0.90 = 0.10. Since we are looking for t_{α/2}, divide α by 2 to get α/2 = 0.10 / 2.
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 and the calculated degrees of freedom (df).
5. Step 5: Verify the critical value. Ensure that the value obtained matches the confidence level and degrees of freedom provided in the problem.