Question

What does it mean to say that we are going to use a sample to draw an inference about a population? Why is a random sample so important for this process? If we wanted a random sample of students in the cafeteria, why couldn’t we just choose the students who order Diet Pepsi with their lunch? Comment on the statement, “A random sample is like a miniature population, whereas samples that are not random are likely to be biased.” Why would the students who order Diet Pepsi with lunch not be a random sample of students in the cafeteria?

Answer 1

a) To get the value of Population parameter like Population mean or Population standard deviation is very difficult. To evaluate Population we need to draw a random sample which will help us to draw inference about population. For example we can not evaluate whole bag of rice . So we draw small sample of rice to know how is quality of whole bag of rice.

Random sample is important because it will be free from biasedness. Non random sample is biased and can not estimate population accurately.

Because then we are doing convenience sampling which is NON RANDOM SAMPLING and this will mislead the result because it will be biased.

Random sample is unbiased because it gives equal chance of selection to each individual of population. For example if we want to check the performance of a school we select only those students who get good marks in exam will lead to wrong or biased result. But if we select students randomly by using any random method like (Random number table) then the average of the sample we will get will be unbiased and will represent school performance on average.

The students who order Diet Pepsi with lunch not be a random sample of students in the cafeteria because the researcher selected the students on the basis of his convenience. It may be possible on that day students who order Diet Pepsi with lunch are more in number than any other usual day. .So it will be non random sample.