第二部分：统计学 作为SG50庆祝活动的一部分，当地的一个基层组织邀请了社区居民观看一部关于1964年种族暴动的电影。

1. Describe the establishment of quotas based on a characteristic.

The reporter decides on a demographic characteristic (such as gender or age group) and divides the sample of $15$ people into specific quotas for each category.

2. Describe the non-random method of data collection.

He then approaches people at the event venue on a convenience basis (e.g., stopping people as they enter or leave) and interviews them until the required quota for each category is completely met.

1. Calculate the sample size to be selected from each age group (stratum) to ensure proportional representation.

Total number of residents $= 130 + 195 + 260 + 65 = 650$

Sampling fraction $= \frac{30}{650}$

Number of residents to select from each age group:

• Below 21 years old: $130 \times \frac{30}{650} = 6$
• 21 - 35 years old: $195 \times \frac{30}{650} = 9$
• 36 - 50 years old: $260 \times \frac{30}{650} = 12$
• Above 50 years old: $65 \times \frac{30}{650} = 3$

2. Describe the random selection procedure within each stratum.

Number the residents in each of the 4 age groups from $1$ to $N$, where $N$ is the number of residents in that group. For each group, use a random number generator to select the required number of unique random integers. The residents corresponding to these selected numbers will form the sample and be contacted through telephone.

3. State a disadvantage of this method compared to quota sampling.

A disadvantage is the problem of non-response (e.g., selected residents not picking up the phone or refusing to give feedback). Unlike quota sampling where an uncontactable person is simply replaced by the next available willing individual in that age group, stratified random sampling requires specific selected individuals to be chased up, which makes reaching the exact sample size of 30 difficult and time-consuming.