In order to evaluate the performance of a certain brand of alkaline battery, res

Question

In order to evaluate the performance of a certain brand of alkaline battery, researchers at a consumer testing organization took a random sample of 152 new 1.5 volt AA batteries. Each of the batteries was subjected to the same pattern of discharge, which was designed to simulate typical moderate use. A battery's lifetime was obtained as the time for the output to drop to 0.9 volt. The mean lifetime of these 152 batteries was 46.7 hours and the standard deviation was 13.3 hours. The industry standard for lifetime of such batteries is 45 hours. Using a 0.06 level of significance what kind of evidence do these data give that this brand of battery has mean lifetime that exceeds the industry standard? What is the P-value of the above testing procedure? What is the general meaning of the P-value of a hypothesis testing procedure?

Explanation / Answer

In electricity, a battery is a device consisting of one or more electrochemical cells that convert stored chemical energy into electrical energy.[1] Since the invention of the first battery (or "voltaic pile") in 1800 by Alessandro Volta and especially since the technically improved Daniell cell in 1836, batteries have become a common power source for many household and industrial applications. According to a 2005 estimate, the worldwide battery industry generates US$48 billion in sales each year,[2] with 6% annual growth.[3] There are two types of batteries: primary batteries (disposable batteries), which are designed to be used once and discarded, and secondary batteries (rechargeable batteries), which are designed to be recharged and used multiple times. Batteries come in many sizes, from miniature cells used to power hearing aids and wristwatches to battery banks the size of rooms that provide standby power for telephone exchanges and computer data centers. Batteries are classified into two broad categories, each type with advantages and disadvantages.[31] Primary batteries irreversibly (within limits of practicality) transform chemical energy to electrical energy. When the initial supply of reactants is exhausted, energy cannot be readily restored to the battery by electrical means.[32] Secondary batteries can be recharged; that is, they can have their chemical reactions reversed by supplying electrical energy to the cell, restoring their original composition.[33] Some types of primary batteries used, for example, for telegraph circuits, were restored to operation by replacing the components of the battery consumed by the chemical reaction.[34] Secondary batteries are not indefinitely rechargeable due to dissipation of the active materials, loss of electrolyte and internal corrosion.

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