SOLUTION: A manufacturer claims that the mean lifetime of lithium batteries is more than 1400 hours. A homeowner selects 25 of these batteries and finds the mean lifetime to be 1580 hours wi

Question 1159163: A manufacturer claims that the mean lifetime of lithium batteries is more than 1400 hours. A homeowner selects 25 of these batteries and finds the mean lifetime to be 1580 hours with a standard deviation of 80 hours. Test the manufacturer's claim. Use α = 0.05. Assume the distribution is normal. Use the Confidence Interval method. Exact value of the standard deviation is not known.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!

Ho: Lifetime is 1400 hours
Ha: Lifetime is not 1400 hours
alpha=0.05 p{reject Ho|Ho true}
test is t0.975, df=24)
critical value is t>2.064
for 95%CI use mean+/-t*s/sqrt(n)
this is 1580+/-2.064*80/sqrt(25)
half-interval is 33 hours
CI is (1547, 1613)
1400 does not lie in the interval and therefore can assume the mean lifetime is not 1400 hours but rather longer.
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