Question 1182940
1) The test statistic is


{{{t = (X-bar - mu)/(s/sqrt(n))}}}


2)  From the given info, X-bar = 29, s = 5, n = 15, and {{{mu = 31}}}.

Then {{{t = (X-bar - mu)/(s/sqrt(n)) = (29-31)/(5/sqrt(15)) = -1.5492}}}, to 2 d.p.

Now {{{t[0.005] = 2.977}}}, and {{{-t[0.005] = -2.977}}}.  

Since 

{{{-t[0.005] = -2.977 < t < 2.977 = t[0.005] }}}, 

then according to the firm's quality standard, 
there is no reason to conclude that the battery lifetime is other than 31 hours.