Question

Key concepts in statistics for business decision making are “Population”, “Census”, “Random Sample” and “Sampling Error”.

The Foodmart CEO (Chief Executive Officer) has very little knowledge about statistics and believes that a sample should not be used for gathering data as a sample cannot provide accurate information about a whole population.

Explain briefly each of the terms given below, drawing on the pleminary comments from the previous page. In your answers below, use the Foodmart supermarkets to provide examples.

(a) Define the term “population”, and explain what the population is for the Foodmart situation outlined in the Preliminary Comment.

(b) Define the term “census”, and explain what this would mean in studying supermarkets in the Foodmart chain.

(c) Define the term “random sample”. In your answer also include an explanation of a “biased sample”. Also explain how you would take a random sample of 150 supermarkets for Foodmart.

(d) Define the term “Sampling Error” and explain in plain language for the CEO how we can manage this if we have a random sample.

Answer 1

Solution:

a) Population: In statistics, a population is a set of similar items or events which is of interest for some question or experiment. Or population is also defined as the all items under the study or consideration. In foodmart situation, the set of all foodmarts makes the population.

b) Census: A census is a survey conducted on the full set of observation objects belonging to a given population or universe. Context: A census is the complete enumeration of a population or groups at a point in time with respect to well defined characteristics: for example, population, production, traffic on particular roads. In foodmart chain, census is the study of each and every foodmart under consideration.

c) Random Sample: A random sample is a sample that is chosen randomly. It could be more accurately called a randomly chosen sample. Random samples are used to avoid bias and other unwanted effects.

Bias in statistics: In statistics, sampling bias is a bias in which a sample is collected in such a way that some members of the intended population have a lower or higher sampling probability than others. In other words, sampling bias exists if probability of selction for items from population not same.

If you want to draw random sample of 150 from population, you have to check the population size. Means how many food marts are there for CEO's consideration. Then generate 150 random numbers using random number table or any software. Then select the foodmarts as random numbers.

Eg. If you have 500 foodmarts under consideration, then generate 150 random numbers between 1 to 500. And select the marts as per drawn 150 random numbers.

d) In statistics, sampling error is the error caused by observing a sample instead of the whole population. The sampling error is the difference between a sample statistic used to estimate a population parameter and the actual but unknown value of the parameter.

ex: If we are interested in the average income of food marts under consideration. Then we draw a sample of foodmarts from our population and take average. But if our selected sample is not good then it will not provide a good estimate for foodmart income. So you have take sample of foodmarts which descibes all characteristics of population. Means foodmarts should be choosen from all different areas, locations, cities,etc.