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The life in hours of a battery is known to be approximately normally distributed. The manufacture claims that the average battery life exceeds 40 hours. A random sample of 10 batteries has a mean life of $40.5$ hours and sample standard deviation $\mathrm{s}=1.25$ hours. Carry out a test of significance for $H_{0}: \mu=40 \mathrm{hrs}$ vs $H_{1} \mu>40 \mathrm{hrs} . \alpha=0.05$
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