A More Extensive Tabulation of T Critical Values Than What $( \bar { x } - .687 s / \sqrt { 21 } , \bar { x } + 1.725 s / \sqrt { 21 } )$

Essay

A more extensive tabulation of t critical values than what appears in your text shows that for the t distribution with 20 df, the areas to the right of the values .687, .860, and 1.064 are .25, .20, and .15, respectively. What is the confidence level for each of the following three confidence intervals for the mean μ of a normal population distribution? Which of the three intervals would you recommend be used, and why?
a. $( \bar { x } - .687 s / \sqrt { 21 } , \bar { x } + 1.725 s / \sqrt { 21 } )$
b. $( \bar { x } - .860 s / \sqrt { 21 } , \bar { x } + 1.325 s / \sqrt { 21 } )$
c. $( \bar { x } - 1.064 s / \sqrt { 21 } , \bar { x } + 1.064 s / \sqrt { 21 } )$