Suppose we want to calculate a 94% confidence interval for a sample mean with a sample size n=54. We ignore the variance of the variable in the population. What is the numerical value corresponding to the order quantile used in calculating the confidence interval? Show your approach

1. Determine the confidence level: 94%.

2. Calculate the significance level: \alpha = 1 - 0.94 = 0.06 .

3. Divide the significance level by 2 to find the tail probability: \alpha/2 = 0.03 .

4. The degrees of freedom for our sample is n - 1 = 54 - 1 = 53 .

5. Look up the value in the t-distribution table corresponding to 53 degrees of freedom and a two-tailed probability of 0.06. Alternatively, you can use statistical software or a calculator.

The t-score that corresponds to a cumulative probability near (1 - 0.03) for 53 degrees of freedom is approximately 1.922 .

Thus, the numerical value is 1.922 .