### Section B: Statistics [60 marks] In the last election, …

Section B: Statistics [60 marks]

In the last election, there were speculations from unofficial sources before the counting of votes is completed. For the current election, to prevent unnecessary speculations, the election office of Sunny Island will be conducting a sample count in each electoral division after voting is done. Each electoral division has a different number of registered voters and a sample of 400 votes will be sampled from each electoral division.

(i)
Identify and describe an appropriate method to obtain the sample.
(ii)
State an advantage and a disadvantage of the sampling method used in part (i).

Population and simple random sample 中文

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Worked solution

5(i)

1. Identify the appropriate sampling method.

Method: Systematic Sampling

2. Define the sampling interval.

Let $N$ be the total number of votes cast in the electoral division.
Calculate the sampling interval $k = \lfloor \frac{N}{400} \rfloor$ .

3. Describe the selection process.

Randomly choose a number $r$ between $1$ and $k$ inclusive.
Select the $r$ -th vote, and subsequently pick every $k$ -th vote (i.e., $r+k$ , $r+2k$ , ...) until $400$ votes have been sampled.

Answer

Method: Systematic Sampling

Description:

Let $N$ be the total number of votes in the electoral division.
Determine the sampling interval $k = \lfloor \frac{N}{400} \rfloor$ .
Randomly select a starting vote from the 1st to the $k$ -th vote, let this be the $r$ -th vote.
Select every $k$ -th vote thereafter (i.e., the $(r+k)$ -th, $(r+2k)$ -th vote, etc.) until exactly 400 votes are obtained.

5(ii)

1. State an advantage of the sampling method (Simple Random Sampling)

Advantage: The sample is unbiased because every vote in the electoral division has an equal chance of being selected.

2. State a disadvantage of the sampling method

Disadvantage: It is time-consuming and tedious to implement, as every single vote in the electoral division needs to be assigned a number in order to randomly select 400 of them.

Answer

Advantage: The sample is unbiased as every vote has an equal chance of being selected.
Disadvantage: It is time-consuming and tedious to number every single vote in the electoral division to perform the random selection.

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