Question 1039619
a.	
For a two-tailed test using a 0.01 significance level, the critical t-values (with df = 11) are -3.106 and 3.106.
Decision rule:  Reject {{{H[0]}}} if the test statistic is in the interval ({{{-infinity}}}, -3.106) or (3.106, {{{infinity}}}).


b.  Test statistic.
{{{t = (X[s] -400)/(sigma/sqrt(n)) = (407 -400)/(6/sqrt(12)) = (7*sqrt(12))/6 = 4.04}}}

{{{X[s]}}} is the sample mean.


c.  Since t = 4.04 lies in the interval  (3.106, {{{infinity}}}),  reject {{{H[0]}}}.