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Problem Number Solution
1
Answer:
(a)
Density of people per square kilometer. Among the given answer options, this is the unit of measure, which can be counted (data item), which is a statistical variable.
(b)
The population includes all observations or cases. In the context of density of people per square kilometer, the set of densities of people per square kilometer of all countries is the population.
2 Answer:
(a)
Ordinal. The ratings are ordered, but the points on this scale are not equidistant.
(b)
This is a stratified random sampling – the researcher divided the data into strata by the program they have participated in, and then randomly sampled students from each strata.
3
Answer:
(a)
True. Because the variance of a data set of size n can be expressed as follows:
Obviously, zero is possible only when all X values are equal to the mean value, which is only possible, when all X are equal.
(b)
No, this is false. In fact, the median of a normal distribution is equal to its mean and mode. However, it can be any number – positive, or negative, or zero. It depends on concrete normal distribution parameters.
4
Answer:
(a)
This is cluster sampling.
(b)
The researcher divided the population of interest on clusters – individual fifth grade classrooms. Then, a simple random sample of clusters was collected (10 clusters), and all data from these clusters were used.
5
Answer:
(a)
t-test for two independent samples
(b)
Since two samples are independent from each other (four- and six-cylinder cars are obviously independent), we can use t-test for independent samples. Other options are unfit. Correlation is used to measure the strength of association, z-test for population mean is used when the standard deviation of population is known, and t-test for dependent samples is used only when the samples are dependent.
6
Answer:
(a)
ANOVA
(b)
The main reason to use ANOVA is because the independent variable (weight loss program) consists of more than 2 groups (namely, 10), and the dependent variable is weight change, which is measured on a continuous numerical scale (in pounds, kg, etc.). These are one of the conditions to use ANOVA. Other listed techniques are not usable in this situation.
7
Answer:
(a)
x ̅=1/10 ...
1
Answer:
(a) (2) Density of people per square kilometer
(b) (3) Set of densities of people per square kilometer of all countries
2 Answer:
(a) (3) ordinal
(b) (1) cluster
3
Answer:
(a) TRUE
(b) TRUE
4
Answer:
(a) cluster sampling is used
(b) they divides the population into separate groups. Called cluster. Then select 10 cluster randomly and accessed the students from the sampled clusters.
5
Answer:
(a) (1) t-test for two independent samples
(b) This is because the test involves ...
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