Final answer:
The positive critical value is found using a t-distribution table or calculator function (invT) specific to an alpha level of 0.01 and 18 degrees of freedom (since the sample size is 19). This value would be higher than for an alpha level of 0.05.
Step-by-step explanation:
To find the positive critical value for a two-tailed t-test with a sample size of 19 at an alpha level (α) of 0.01, you would use a t-distribution table or a calculator's inverse t function. Since the sample size is 19, the degrees of freedom (df) for the t-test would be 18 (n - 1). Looking up the two-tailed critical value for α = 0.01 in a t-distribution table or using a calculator's invT function for the 99% confidence level (1 - α/2 = 0.995), you would find the positive critical value. The exact number can vary slightly based on the source, but it will be a value that corresponds to that high level of confidence for 18 degrees of freedom.
For example, if we were considering the t-value at a 95% confidence interval for 19 degrees of freedom (α = 0.05), we might find a t-value of 2.093. However, since the alpha level here is much smaller (α = 0.01), the critical value would be higher than 2.093.