Question

1. Professor Trelawney’s research assistant is hard at work again. This time the Professor has asked the assistant to begin some basic inferential analysis. The assistant has been given a data set consisting of 45 observations taken by the professor for a study into neighborhood design and crime. The assistant is now at the point of trying to apply one of the theoretical distributions to the results obtained in the first round of analysis. Should the assistant try to apply the principles of the Z distribution or those associated with the t distribution? Why?

2. Explain why researchers do not usually examine populations directly.

3. Define representativeness. Why is this concept important? What is the advantage of having data that are representative?

Answer 1

1) The assistant has been given a data set consisting of 45 observations taken by the professor for a study into neighborhood design and crime.

The assistant is now at the point of trying to apply one of the theoretical distributions to the results obtained in the first round of analysis.

Should the assistant try to apply the principles of the Z distribution or those associated with the t distribution? Why?

Here assistant should have to use Z distribution instead of t, because our sample size of the data is greater than 30 .which is large enough to use the Z distribution.

2) Explain why researchers do not usually examine populations directly.

Answer:- Researchers usually used a sample from the population. because examining the population would be a tedious task. we cannot find all observations in population or maybe it is not possible to get all observation of population for e.g for blood group study taking whole blood of the body.

It is a very time-consuming task to examine the population. it may be costly also.

for all the above reasons researchers usually do not examine the population directly.

3) Define representativeness. Why is this concept important? What is the advantage of having data that are representative?

A representative sample is a subset of a population that seeks to accurately reflect the characteristics of the larger group.

So the sample said to be representative of population if it is a group or set chosen from a larger statistical population or group of factors or instances that adequately replicate the larger group according to whatever characteristic or quality is under study.

If the concept of representativeness is not there we have to find all population observation & which becomes a tedious task. as mentioned in q.2)

advantage of having data that are representative

1) Do not have to examine the whole population

2) accurate estimate will be provided with less effort

3) time will be saved

4) money will be saved

5)manpower will be reduced.