A company has developed a new battery, but the average lifetime is unknown. In order to estimate this average, a sample of 110 batteries is tested and the average lifetime of this sample is found to be 200 hours. The 200 hours is the value of a: A) parameter. B) statistic. C) sampling frame. D) population
The correct answer and explanation is:
The correct answer is B) statistic.
A statistic is a numerical value that is computed from a sample of data. In this case, the 200 hours represents the sample mean, which is an estimate of the average lifetime of the batteries in the population. A sample mean, such as this one, is a statistic because it is based on data taken from a subset or sample of the total population.
In contrast, a parameter would refer to a numerical value that describes the entire population, such as the true average lifetime of all batteries produced by the company. However, since the true population mean is unknown and we are only given the sample mean, the correct term here is statistic.
A sampling frame refers to the actual list or set of all items or individuals from which a sample is drawn. It is not a numerical value but rather a representation of the population from which the sample is selected.
The population refers to the complete set of all possible items or individuals that a researcher is interested in studying. For instance, the population could refer to the lifetime of all batteries ever produced by the company. However, in this case, since we are dealing with a sample (the 110 tested batteries), the population is not represented by the 200 hours, but rather by the lifetime of all batteries produced.
So, in summary, the 200 hours is the average lifetime found from the sample and, thus, is a statistic, which is used to estimate the population parameter (in this case, the average lifetime of all batteries).