Answer to Question #263538 in Statistics and Probability for JAMES

Question

a. Differentiate between probability sampling and non-probability sampling.

(2 marks)

b. Give any three reasons for sampling over a census. (3 marks)

c. Plot a scatterplot with at least 5 data point, given that the correlation

coefficient 𝑟 = −1. (2 marks)

d. Differentiate between parametric and non-parametric tests. (2 marks)

e. The table below shows a relationship between the number of times an

advertisement was aired and digital camera sales. Use sales as the dependent

variable. Draw a scatter diagram. (2 marks)

Number of Airing Sales “000”

4 15

2 8

5 21

6 24

3 17

f. If a company employs 3500 people and if a random sample of 175 of these

employees has been taken by systematic sampling, what is the value of k?

(2 marks)

g. How does sampling error occur? (2 marks)

Answer 1

a.

Probability sampling is a sampling technique, in which the subjects of the population get an equal opportunity to be selected as a representative sample.

Nonprobability sampling is a method of sampling wherein, it is not known that which individual from the population will be selected as a sample.

b.

1.

Sampling requires less time and labor than census because only a part of

the population has to be examined. The sampling results also can be

analysed much faster;

2.

Sampling usually results in reduction in cost in terms of money and man

powers. The total cost of the sample survey is expected to be much smaller

than a complete census;

3.

There is generally a greater scope in a sample survey than in census.

Some inquiries may require highly trained personnel or specialized

equipment for collection of data, then the census may be inconceivable

d.

Parametric tests are based on assumptions about the distribution of population from which the sample was taken. Nonparametric tests are not based on assumptions, that is, the data can be collected from a sample that does not follow a specific distribution.

f.

The interval can be calculated by dividing the population size by the desired sample size

$$k=\dfrac{3500}{175}=20$$

g.

A sampling error occurs when the sample used in the study is not representative of the whole population. 

e.

c.

if the correlation coefficient 𝑟 = −1, then there is the strong negative linear relationship.

for example:

x y

5 15

6 14

7 13

8 12

9 11