Consumer Reports gave a report about the life (hours) of size AA batteries in to

Question

Consumer Reports gave a report about the life (hours) of size AA batteries in toys. A total of 16 toys were tested which gave a mean life of 3.58 hours with sample standard deviation of 1.85 hours. Find a 98% confidence interval for the mean life of AA batteries. The packaging for the batteries claim t the AA batteries last around 5 hours in toys. Does the sample differ from the claim? alpha = .02

Explanation / Answer

Given n=16, xbar=3.58, s=1.85 (a) =0.02, t(0.01, df=n-1=16-1=15) = 2.6 (check student ttable) xbar ± t*s/n --> 3.58 ± 2.6*1.85/sqrt(16) --> ( 2.3775, 4.7825) (b) The test hypothesis is Ho:5 =0.02, t(0.01, df=n-1=16-1=15) =-2.602 (check student ttable) The test statistic is t=(xbar - )/ (s/n) =(3.58 - 5)/ (1.85/sqrt(16)) =-3.07 Since t = -3.07 < -2.602, we reject Ho.

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