Solution

The $\text{variables}$ are the topics that were investigated.

$$\textbf{variables}

$\textbf{Categorical/qualitative}$ variables places the individuals into a category, while a $\textbf{quantitative}$quantitative variable is a numerical variable.

$\textbf{Discrete}$ data are restricted to defined separated values, for example integers or counts. $\textbf{Continuous}$ data are not restricted to defined separate values, but can occupy any value over a continuous range, for example decimal, rational or real numbers.

The $\textbf{population}$ contains the set of measurements about which we want to collect information.

A $\textbf{sample}$ is the part of the set of measurements of which information was actually collected.

SOLUTION

(a) We are interested in the survival time after the onset of a particular type of cancer and a particular regiment of radiotherapy, which implies that the variable of interest is "Survival time".

(b) The survival time can take on numerical values, thus the variable is quantitative. Moreover, the survival time can also take on decimal values (for example, 0.5 years or 1.75 months) and thus variable is also continuous.

(c) We are interested in the survival times of all cancer patients that undergo a particular regiment of radiotherapy, which is thus the population of interest.

(d) The sample could potentially consist of all cancer patients that passed away in the past year.

(e) The sample is not a true random sample and thus these cancer patients could have certain characteristics in common, which are not shared by all people in the population. For example, these cancer patients could have the most sever cases of cancer and thus there survival times will then be much less than those with less sever cases of cancer.

Answer

(a) Survival time

(b) Quantitative continuous

(c) Survival times of all cancer patients that undergo a particular regiment of radiotherapy

(d) All cancer patients that passed away in the past year.

(e) These cancer patients could have the most sever cases of cancer and thus there survival times will then be much less than those with less sever cases of cancer.

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