Question 1090504: In the study of fingerprints, an important quantitative characteristic is the total ridge count for the 10 fingers of an
individual. The University Management and Technology uses thousands of fans each year. The brand of fans it currently
has a mean life of 9000 hours. A manufacturer claims that its new brand of fans, which cost the same as the brand the
university currently uses, has a mean life of more than 9000 hours. The university has decided to purchase the new brand
if, when tested, the test evidence supports the manufacturer’s claim at the .05 significance level. Suppose 64 fans were
tested with sample mean x 9200 hours and standard deviation S = 800 hours.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! This is a one-tail test; assume random sample from normal distribution and s is an unbiased estimator of sigma.
Ho: fans last same or less than old ones
Ha: fans last longer
alpha=0.05 P{reject Ho|Ho true}
test statistic is a t df=63, 0.95
Critical value is t>1.98
calculation is t=(9200-9000)/800/sqrt (64)
this is 200/100 or +2
This falls beyond the range of the critical value, so the null hypothesis is rejected and the manufacturer's claim is supported.
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