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A company claims that the average battery life of its rechargeable battery is 18 hours. A random sample of 40 batteries has a sample mean of 17.2 hours and a sample standard deviation of 2.5 hours. The test is conducted at a 5% significance level. Since the sample size is relatively large ((n=40)), the z-test for the population mean can be used. The hypotheses are: [ H_0:\mu=18 ] [ H_1:\mu\neq18 ] Here, (H_0) represents the manufacturer’s claim, while (H_1) indicates that the true average battery life is different from 18 hours. Since the alternative hypothesis is two-tailed, the 5% significance level is divided equally between the two tails. Given: [ n=40,\quad \bar{x}=17.2,\quad s=2.5,\quad \mu_0=18 ] The test ____ ______ _________ ________ ______ ___ ____ ________ _______ ___ ____.
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