﻿ Statistics Counting Rules Worksheet | Problems & Solutions

# Statistics Counting Rules Worksheet

Statistics Counting Rules Worksheet
• Page 1
1.
Select the correct statement(s).
I. A population is a group of subjects selected from a sample.
II. A sample is a group of subjects selected from a population.
III. A population consists of all subjects that are under study.
IV. Statistical studies always use samples.
 a. II and III only b. II, III and IV only c. III and IV only d. I and IV only

#### Solution:

A population consists of all subjects that are under study.

A sample is a group of subjects selected from the population for study.

Sample selection is done when it is not practically possible to study the entire population.

Sample selection is not done always.

So, only II and III are correct.

2.
Select the items described as population (P) or samples (S).
I. Five girl students each from each grade of the school.
II. Every fifth car produced in a factory.
 a. I - (S), II - (S), III - (P). b. I - (S), II - (S), III - (S). c. I - (P), II - (S), III - (P). d. I - (P), II - (P), III - (S).

#### Solution:

I and II represent samples.

All graduates in USA is population.

The answer is I - (S), II - (S), III - (P).

3.
Select the correct statements.
I. Samples are used when the population is too small.
II. Samples are used when the population is too large.
III. Samples are used when the time available for a study is limited.
IV. Samples are used only to reduce cost.
 a. II and III only b. II, III and IV only c. I only d. IV only

#### Solution:

Samples are used when the population is too large.

Samples are used when the time available for a study is limited.

Cost reduction is not the only objective of sampling.

The correct statements are II and III only.

4.
What are the different types of sampling?
 a. Direct sampling, indirect sampling, random sampling and systematic sampling. b. Telephone survey, mail questionnaire, personal interview and direct observations. c. Systematic sampling, unbiased sampling, random sampling and simple sampling. d. Random sampling, systematic sampling, stratified sampling and cluster sampling.

#### Solution:

The sampling techniques are random sampling, systematic sampling, stratified sampling and cluster sampling.

5.
What shall be the most important objective of selecting sample from a population?
 a. Sample selection shall be cost saving. b. Each subject in the population shall have an equally likely chance of being selected. c. Maximum number of samples shall represent the population. d. Sample shall be selected through direct observation.

#### Solution:

The sample is to be selected so that it truly represents the population.

Each subject in the population is qualified to be a sample.

Sample selection shall be in such a way that each subject in the population shall have an equally likely chance of being selected.

6.
Every fourth passenger boarding the aircraft was requested to fill up a small questionnaire to find out the customer satisfaction. The data collection methodology is _______ sampling.
 a. stratified b. systematic c. random d. cluster

#### Solution:

Every fourth passenger boarding the aircraft was requested to fill up a small questionnaire to find out the customer satisfaction. The data collection methodology is systematic sampling.

7.
The seat numbers of all the passengers travelling in an aircraft were noted down and a few were selected through a lot. The selected passengers were requested to convey their opinion on the service of the airlines by filling up a questionnaire. What is the sampling method used in this case?
 a. systematic b. cluster c. random d. stratified

#### Solution:

The seat numbers of all the passengers travelling in an aircraft were noted down and a few were selected through a lot. The selected passengers were requested to convey their opinion on the service of the airlines by filling up a questionnaire. The sampling method used in this case is random sampling.

8.
Five students from each class of the school were interviewed to find out their opinion on the transportation facilities. What is the type of sampling used?
 a. cluster b. stratified c. systematic d. random

#### Solution:

Five students from each class of the school were interviewed to find out their opinion on the transportation facilities. The type of sampling used here is stratified sampling.

9.
A survey was conducted among the patients of two hospitals in the city to assess the general facilities in health care. What type of sampling is used?
 a. cluster b. stratified c. systematic d. random

#### Solution:

A survey was conducted among the patients of two hospitals in the city to assess the general facilities in health care. The type of sampling used here is cluster sampling.

10.
A manufacturing unit produces 2000 electric bulbs every month. Samples of the bulbs are to be tested for any manufacturing defects. What is the best sampling methodology for testing?
 a. cluster sampling b. random sampling c. systematic sampling d. full population

#### Solution:

Testing of entire population is not practical due to limitations in cost and time.

Cluster sampling will not provide information on a particular batch and may not reflect the true stage of the manufacturing process.

Random sampling is possible, but is a continuous process.

Systematic sampling is most suited.