SOLUTION: The distribution of battery lives are assumed to be approximately normal and a manufacturing firm claims that the batteries used in their electronic games will last an average of 3

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Question 1182940: The distribution of battery lives are assumed to be approximately normal and a manufacturing firm claims that the batteries used in their electronic games will last an average of 31 hours. To maintain this average, 15 batteries are tested each month. If the computed t-value falls between. -t0.005 and t0.005 , the firm is satisfied with its claim. If the firm draws a sample that has a mean of 29 hours and a standard deviation of 5 hours,
1) Find the test statistics
2) What conclusion should the firm draw?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
1) The test statistic is

t+=+%28X-bar+-+mu%29%2F%28s%2Fsqrt%28n%29%29

2) From the given info, X-bar = 29, s = 5, n = 15, and mu+=+31.
Then , to 2 d.p.
Now t%5B0.005%5D+=+2.977, and -t%5B0.005%5D+=+-2.977.
Since
-t%5B0.005%5D+=+-2.977+%3C+t+%3C+2.977+=+t%5B0.005%5D+,
then according to the firm's quality standard,
there is no reason to conclude that the battery lifetime is other than 31 hours.