Find the value ta/2 for constructing a 95% confidence interval for 𝜇 if we draw a sample of size 15 from a normal population with 𝜎 unknown.

To find the value of tα/2 for constructing a 95% confidence interval for 𝜇, we need to follow these steps:

1. Identify the degrees of freedom (df): The degrees of freedom for a sample is the sample size minus 1. In this case, df = 15 - 1 = 14.

2. Identify the confidence level: In this case, the confidence level is 95%. This means that α = 1 - 0.95 = 0.05.

3. Divide α by 2: Because the t-distribution is symmetric, we divide α by 2 to find the t-value for a two-tailed test. So, α/2 = 0.05/2 = 0.025.

4. Look up the t-value: Using a t-distribution table or an online t-value calculator, look up the t-value that corresponds to 14 degrees of freedom and α/2 = 0.025. The t-value is approximately 2.145.

So, the value of tα/2 for constructing a 95% confidence interval for 𝜇 with a sample size of 15 and 𝜎 unknown is approximately 2.145.