To calculate a 95% confidence interval for a mean, using a sample of 9 data values, the required t-multiplier, correct to 3 decimal places, would be

To calculate a 95% confidence interval for a mean, you would need to use a t-distribution table because the sample size is small (less than 30).

Step 1: Identify the degrees of freedom (df). The degrees of freedom for a sample is always the sample size (n) minus 1. So in this case, df = 9 - 1 = 8.

Step 2: Look up the t-multiplier in the t-distribution table. You want a 95% confidence interval, which leaves 5% in the two tails of the distribution (2.5% in each tail). So, you need to find the t-value for a two-tailed test with df = 8 and alpha level (α) = 0.05/2 = 0.025.

Step 3: The exact t-multiplier value can vary slightly depending on the specific t-distribution table used, but typically, for 8 degrees of freedom and α = 0.025, the t-multiplier is approximately 2.306, correct to 3 decimal places.

So, the required t-multiplier would be 2.306.