Final answer:
Researchers attempting to establish a confidence interval with a t-distribution must use the standard ta/2 value associated with their desired confidence level and degrees of freedom. The value of 0.31 mentioned does not correspond to conventional confidence levels, which usually have higher ta/2 values for any realistic degree of freedom.
Step-by-step explanation:
The confidence level associated with a confidence interval when using a particular t distribution is determined by the ta/2 value and the degrees of freedom. If the student is using a ta/2 value of 0.31 as their favourite number, this does not correspond to a conventional confidence level. Typically, the ta/2 value for common confidence levels such as 90%, 95%, or 99% is found using a t-distribution table or a calculator's in it function.
For example, with a sample size of 1470 observations, the degrees of freedom would be 1469. To find the confidence level corresponding to a particular ta/2 value, one would use the invT calculator function or consult a t-distribution table. The value of 0.31 does not match standard ta/2 values for common confidence levels which are known to be higher - it more likely corresponds to a value on the very high end of the confidence level spectrum, but without more context or the correct ta/2 value for the number of degrees of freedom we can't determine the exact confidence level.
To properly calculate a confidence interval with a meaningful confidence level, researchers need to select a standard ta/2 value that corresponds to their desired confidence level and degrees of freedom. For example, in a normal distribution for a 95% confidence interval with 19 degrees of freedom, ta would be approximately 2.093.