Which t-value corresponds to α/2 for a confidence level of 95% with 69 degrees of freedom?

To determine the t-value that corresponds to α/2 for a 95% confidence level with 69 degrees of freedom, we first need to understand the concept of the t-distribution and how it applies to confidence intervals.

For a confidence level of 95%, α is 0.05. Since we are looking for the t-value at α/2, we calculate α/2, which is 0.025. This means we are interested in the t-value that corresponds to the upper tail of the t-distribution where the cumulative probability is 0.975 (since 1 - α/2 = 0.975).

Using a t-table or statistical software for 69 degrees of freedom, we look up the t-value that matches this cumulative probability. The correct t-value for 69 degrees of freedom at the 0.975 cumulative probability mark is approximately 1.9949.

This value is critical because it is used in constructing confidence intervals for means when the sample size is relatively small or when the population standard deviation is unknown, which is generally the case in business statistics when analyzing sample data.

Therefore, the answer, which reflects the correct t-value for a 95% confidence level with 69 degrees of freedom,