Question

Use the following information to answer the next 3 questions. Parents of children with developmental disorders can apply for federal funding, to help pay for psychosocial rehabilitation. A sociologist working for the annual Current Population Survey wants to know the percentage of applicants for this funding who are in poverty. She needs a sample of applicants from across the U.S., so she groups all of the applications by state and randomly selects applicants from each state. She calculates the percentage of applicants in her sample that are in poverty. Is this percentage a parameter or a statistic, and why?

Answer 1

Solution

Back-up Concepts

Parameter vs Statistic

Parameter is a function of the population and hence its value is obtained using all the values in the population.

Statistic is a function of the sample and hence its value is obtained using all the values in the sample.

For example, if the mean test score is calculated, say µ, for the full class averaging the test scores of all the students in the class, µ is a parameter.

But, if a random sample of 10% of the students of the class is taken and their average score, say Xbar, is calculated, Xbar is a statistic.

Now, to work out the solution,

Going by the concepts given above, the percentage of applicants in the sociologist’s sample that are in poverty is a statistic. Answer

Just to make the point still clearer,

Imagine the sociologist collected all the applications for funding over the entire U.S. [well, one does not waste time and effort doing that!!!] and found out the percentage, say p, then p would be the parameter.

DONE