1. Define each of the following statistical terms:
A. Descriptive statistics.
B. Statistical inference.
C. Population.
D. Sample.
E. Parameter.
F. Statistic.
ANS:
A. Descriptive statistics deals with methods of organising, summarising and presenting data in a
convenient and informative way.
B. Statistical inference is the process of making an estimate, prediction or decision about a population parameter, based on sample data.
C. A population is the group of all items of interest to a statistics practitioner. It is frequently very large and may, in fact, be infinitely large.
D. A sample is a set of data drawn from the population.
E. A parameter is a summary measure that is computed from a population.
F. A statistic is a summary measure that is computed from a sample to describe the corresponding characteristic of the population.
PTS: 1 DIF: Easy TOP: Key statistical concepts
2. A manufacturer of televisions claims that fewer than 3% of their products are defective. When 100 televisions were drawn from a large production run, 10% 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 3% refer to the parameter or the statistic?
F. Is the value of 10% a parameter or a statistic?
G. Explain briefly how the statistic can be used to make inferences about the parameter to test the claim.
ANS:
A. The complete production run of the manufacturer.
B. The 100 televisions selected.
C. The proportion of the production run that is defective.
D. The proportion of the sample televisions that is defective.
E. Parameter.
F. Statistic.
G. Because the sample proportion is well above 3%, we conclude that the sample data selected does not support the claim.
PTS: 1 DIF: Moderate TOP: Key statistical concepts
3. A businessman who is running for a vacant city council seat with 2000 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?
ANS:
A. 200/300=0.666, i.e. 66.6%.
B. The political choices of the 2000 registered voters in the given constituency.
C. The political choices of the 300 registered voters in the survey.
D. Statistic.
PTS: 1 DIF: Moderate TOP: Key statistical concepts
4. Consider the population of all pencil manufacturers in the world. Describe any four examples of possible samples that could be taken from this population.
ANS:
Manufacturers of wooden pencils.
Manufacturers of colour pencils.
Manufacturers of graphite pencils.
Australian manufacturers of pencils.
PTS: 1 DIF: Easy TOP: Key statistical concepts
5. Identify each of the following studies as using 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 Melbournian households.