Question: The Arf n' Barf Dog Food Company is interested in estimating the average fat grams per ounce of a new recipe developed by its research department. Accordingly, 80 one-ounce samples of the product are tested with the following results:

\(\sum{{{X}_{i}}}=1,250\) and \(\sum{X_{i}^{2}=24,000}\)

where \({{X}_{i}}\) = fat content (grams) of the ith one-ounce sample observation.

Required: Use this data to construct a 98 percent confidence interval for the mean fat content (grams per ounce) of this recipe.