Question $3$

$[8]$

Determine the appropriate sampling method $($ simple random, stratified, systematic, cluster or convenience$)$ from each of the following sampling survey scenarios. Justify your answer.

$3\mathrm{.}1$ A researcher selects individuals as they are passing through a certain location in shopping mall and ask them questions on matters related to services deliveries and elections.

$3\mathrm{.}2$ Politicians seeking to gauge the attitudes and concerns of their constituents when they report on the number of letters voluntarily sent to them. They divided the population into subgroups $($subgroups with similar characteristics$)$ and selected questions from the entire subgroup. $(2)$

$3\mathrm{.}3$ The names of all the $1000$ children are placed into a computer data base. The computer is then instructed to randomly selects $100$ names. These children and their parents are then contacted.

$3\mathrm{.}4$ A population of $1000$ children is divided into distinct groups based on a relevant characteristic, such as grade level $($six$,$ seven and eight$).$ The researcher then employs a computer to randomly select a predetermined number of individuals from each stratum.

Question $4$

The following are the make of cars sold by a certain car dealer from January $2024$ to March $2024.$

$\backslash$table$[[$BMW$,$TOYOTA,AUDI,BMW$,$VW POLO$],[$FORD$,$HONDA,BMW$,$TOYOTA,BMW$],[$TOYOTA$,$VW POLO,TOYOTA,NISSAN,FIAT$],[$NISSAN$,$MERCEDES BENZ,FORD,TOYOTA,TOYOTA$],[$TOYOTA$,$

AUDI,NISSAN,HONDA,MERCEDES BENZ$],[$BMW$,$TOYOTA,TOYOTA,BMW$,$VW POLO$],[$TOYOTA$,$VW POLO,BMW$,$FORD,BMW$],[$FIAT$,$AUDI,TOYOTA,TOYOTA,TOYOTA$],[$BMW$,$NISSAN,BMW$,$FORD,TOYOTA$]]$

$4\mathrm{.}1$ Draw a bar graph with the counts $($frequencies$)$ and relative frequencies.

$4\mathrm{.}2$ Construct a pie chart.

$4\mathrm{.}3$ Determine the percentage of the make of Ford cars sold by the car dealer?

$4\mathrm{.}4$ Determine the percentage of the make of BMW or VW Polo cars sold by the car dealer?