Question

 

Part I. Provide an example of a population, a sample, a parameter, and a statistic.

Part II. Let’s say researchers are planning a study on COVID-19. They end up with the following kind of variables:

dichotomous, ordinal, categorical, and continuous. Provide one example each of these types of variables in their study. If you had to visualize the ordinal, categorical, and continuous variable, what plots would you use?

Part III. What does the 81st percentile of the data signify?

Part IV. What is a sampling distribution of a statistic? How does this differ from the distribution of some data?

 

Answer 1

i. Examples:
Population: The population of Texas

Sample: 200 people selected from Texas based on random sampling

Parameter: The mean height of all the people living in Texas

Statistic: The mean height of the selected sample

ii. Examples:

Dichotomous: Whether a quarantined individual is Covid 19 positive or not?
Ordinal: Condition of a coronavirus positive patient over the incubation period

Categorical: Labelling of states into different colours based on the quantum of cases in that state.

Continuous: Damages to the pulmonary system of the patient upon infection with the novel coronavirus.

Visualising the variables:

Continous: Line graph

Categorical: Balloon plot

Ordinal: Bar graphs
iii. 81st percentile of data means that 81% of the data points are below that value and 19% are above that value.

iv. Sampling distribution of a statistic is the distribution of all the values which can be taken by the statistic. It is calculated by randomly drawing samples of identical size from the same population.

Sample distribution of the data is basically listing all possible values along with the frequencies which the dataset in question assumes, while the sampling distribution of the statistic is the probability distribution of the statistic of the sample.