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The normally distributed AAA battery life is stated tobe 350 days when used in a clock radio. The Big Charge BatteryCompany has recently modified the AAA batteries so as to extenttheir life. The owner of the company wanted to know if the improvedbatteries really did last significantly longer. A sample of 100 ofthe improved batteries was tested. It was discovered that the meanlife was 362 days and the sample standard deviation was 10 days.The research department decided to conduct the test at the 0.05level of significance whether the modification actually increasedthe life of the AAA battery. What was their decisionrule?