3. The personnel director of a corporation will study the overtime work during the previous year for the 2,575 clerical workers. A sample of 100 of these workers will be chosen at random from the files. The average and the standard deviation of the overtime hours will be calculated and the number of these employees who worked more than 75 hours of overtime will be recorded. For each of the following, state whether it is a statistic or a parameter. (6 pts)
a) The average number of overtime hours for the 2,575 employees.
b) The standard deviation of overtime hours for the 100 workers.
c) The standard error of the average.
d) The proportion of clerical workers in the company who worked more than 75 hours overtime last year
A parameter is a value related to the total population, while statistic only relates to a sample, a portion of the population.
That should help you to come to your own answers.
For each of the following, let's determine whether it is a statistic or a parameter:
a) The average number of overtime hours for the 2,575 employees.
This is a parameter. A parameter is a numerical summary of a population, and in this case, the population is all the clerical workers in the corporation. Since the average is calculated for the entire population of 2,575 clerical workers, it is a parameter.
b) The standard deviation of overtime hours for the 100 workers.
This is a statistic. A statistic is a numerical summary of a sample, and in this case, the sample consists of 100 randomly chosen workers. Since the standard deviation is calculated based on the data from the sample, it is a statistic.
c) The standard error of the average.
This is a statistic. The standard error is a measure of the variability of sample means. It is calculated based on the sample data and provides an estimate of how much the sample mean is likely to deviate from the true population mean. Therefore, it is a statistic.
d) The proportion of clerical workers in the company who worked more than 75 hours overtime last year.
This is a parameter. A parameter represents a numerical summary of a population, and in this case, the population is all the clerical workers in the company. The proportion is calculated for the entire population, so it is a parameter.