The parameter of interest refers to a quantity that describes the population we are interested in studying. The mean and variance of a population are some examples of a parameter we may be interested in studying.
While the parameter refers to quantities that describe the population, a statistic refers to quantities that describe a sample taken from the population. The population mean and population proportion are examples of parameters we may be interested in studying.
Example 1 of Parameter of Interest:
Suppose that a company sells an average of 10000 pieces of equipment per month. The company runs a new advertising campaign in order to increase its sales. How will you decide whether the advertising campaign was effective or not. What is the parameter of interest?
Solution: The parameter of interest in this case is the population mean. If there is a significant increase in the mean/average number of sales per month then we can conclude that the new advertising campaign was effective. We can carry ou the test of significance of mean by using the Z-test.
Example 2 of Parameter of Interest:
Suppose that we are conducting a study to measure the health and eating habits of a population of people. As a part of the study we collect information on the weight of the people in the population. What is the parameter of interest?
Solution: The parameter of interest in this case is the population mean and population standard deviation. We can find the average weight of the people in the population and the standard deviation in order to use it to get an idea abou the overall weight distribution of the population
Example 3 of Parameter of Interest:
Suppose that we have a population of a 1000 people. We wish to know how many of them are heavy drinkers versus those who are not heavy drinkers. What is the paramter of interest?
Solution: The parameter of interest in this case is the population proportion. We wish to know the proportion of people who are heavy drinkers. For example, if the population proportion is 10%, it means that 10% of the people in the population are heavy drinkers.