Question $8[10$ marks$]$

Suppose that you are hired by the Hong Kong government to investigate the car owners regarding their willingness to replace their conventional car to an electric vehicle $($EV$).$ Please answer the following questions:

$1)$ Could you please describe how you plan to conduct the survey? What are the sampling frame and sampling methods? What is the potential bias and what you should be particularly careful about? $[4$ marks$]$

$2)$ Suppose that you plan to use simple random sampling and the sampling frame is perfect and accurate. Our objective is to estimate the average percentage of owners who would like to replace their current cars. Based on the previous survey, we know the percentage is roughly $\backslash (30\backslash \%\backslash ),$ and the standard deviation is $\backslash (5\backslash \%\backslash ).$ Please estimated the number of samples needed such that the acceptable error of the percentage is less than $\backslash (1\backslash \%\backslash )$ in absolute value $($with the level of significance of $5\backslash \%)[4$ marks$]$

$3)$ Do we need to conduct the finite population correction? If yes, please conduct the correction. $[2$ marks$]$