Chapter 1—What is statistics?
MULTIPLE CHOICE
1. A politician who is running for the office of premier in a state with 3 million registered voters
commissions a survey. In the survey, 53.6% of the 5000 registered voters interviewed say they plan to
vote for him. The sample is the:
A
3 million registered voters in the state.
B
5000 registered voters interviewed.
C
53.6 % of, or 2680, voters interviewed who plan to vote for him.
D
46.4% of, or 2320, voters interviewed who plan not to vote for him.
2. A summary measure that is computed from a sample to describe a characteristic of the population is
called:
A
a parameter.
B
a statistic.
C
a population.
D
Both A and C are correct, since they are the same.
3. A summary measure that is computed from a population is called:
A
a parameter.
B
a statistic.
C
a sample.
D
Both A and B are correct, since they are the same.
4. Descriptive statistics deals with methods of:
A
organising data.
B
summarising data.
C
presenting data in a convenient and informative way.
D
doing all of the above.
5. Which of the following statements is not true?
A
One form of descriptive statistics uses graphical techniques.
B
One form of descriptive statistics uses numerical techniques.
C
In the language of statistics, the term population refers to a group of people.
D
Statistical inference is used to draw conclusions or inferences about characteristics of
populations based on sample data.
6. When data is collected in a statistical study for only a portion or subset of all elements of interest, we
are using:
A
a sample.
B
a parameter.
C
a population.
D
both A and B.
7. You ask five of your classmates about their height. On the basis of this information, you state that the
average height of the students in the sample is 170 cm. This is an example of:
A
descriptive statistics.
B
inferential statistics.
C
a parameter.
D
a population.
8. Which of the following is not the goal of descriptive statistics?
A
Summarising data.
B
Displaying aspects of the collected data.
C
Reporting numerical findings.
D
Estimating characteristics of the population.
TRUE/FALSE
1. 25% of a random sample of 300 professional golfers indicate that their parents did not play golf. Based
on this sample, we estimate that 25% of the parents of all professional golfers do not play golf. This is
an example of statistical inference.
2. A local cable TV system using a sample of 500 subscribers finds that 40% of these subscribers watch a
premium channel at least once per day. This is an example of statistical inference as opposed to
descriptive statistics.
3. A summary measure that is computed from a population is called a statistic.
4. A summary measure that is computed from a sample to describe a characteristic of the population is
called a statistic.
5. The main goal of descriptive statistics is to find the characteristics of some data set.
6. Statistical inference is the process of making an estimate, prediction or decision about a population,
based on sample data.
SHORT ANSWER
1. Define each of the following statistical terms:
a. Descriptive statistics.
b. Statistical inference.
c. Population.
d. Sample.
e. Parameter.
f. Statistic.
2. A manufacturer of children toys claims that fewer than 5% of his products are defective. When 500
toys were drawn from a large production run, 8% were found to be defective.
a. What is the population of interest?
b. What is the sample?
c. What is the parameter?
d. What is the statistic?
e. Does the value of 5% refer to the parameter or the statistic?
f. Is the value of 8% a parameter or a statistic?
g. Explain briefly how the statistic can be used to make inferences about the parameter to test the
claim.
3. A businessman who is running for a vacant city council seat with 20 000 registered voters conducts a
survey. In the survey, 200 of the 300 registered voters interviewed say they plan to vote for him.
a. What proportion of the respondents plans to vote for this businessman?
b. What is the population of interest?
c. What is the sample?
d. Is your answer in part (a) above a parameter or a statistic?
4. Consider the population of all tennis players in the world. Define five samples that could be taken
from this population.
5. Identify each of the following studies as either descriptive statistics or inferential statistics:
a. Calculating the relative frequency of Holden Commodore SV6 cars passing by your house
between 7pm and 8pm this evening.
b. Estimating the proportion of households in Melbourne that have at least two dependents, from a
random sample of 100 Melburnian households.
c. Measuring the fuel efficiency of five brand new Holden Commodore SV6 cars in order to find out
whether the average fuel consumption of this make and model is better than 10L/100km.
d. Calculating the proportion of female students in a business statistics class.
e. Estimating the average age of students at La Trobe University from a sample of 200 randomly
selected students.