Chapter-3 DiScuSSion Pick any two sampling designs/techniques discussed in the class and give real-life description of how and where you could draw a sample using those two techniques. For each design make sure you describe the following for this task: 1. Study objective (What is the population and characteristic of interest/study?) 8 Unread 2. How you would draw a sample using one of the techniques for a such a study in practice. Sample Response: Stratified Random Sampling A study was conducted to determine how much viewers of a certain TV program enjoys it. To do this, the production company divides the viewer based into five age groups(5 strata's) - under $$ 18,18-24,25-40,41-55 $$, and $$ 56+ $$. Then they surveyed 50 random viewers from each age group either by using the random digit table, calculator or using technology. Population - all the viewers of the TV program Sample- 50 viewers from each age group surveyed

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### Cluster Sampling

**Study Objective:**  
Investigate the academic performance of high school students in a large city. The population is all high school students, and the characteristic of interest is their overall academic performance (e.g., average test scores).

**Sampling Process:**  
1. **Define Clusters:**  
   The city is divided into clusters based on each high school. Each high school represents one cluster.

2. **Select Clusters at Random:**  
   Suppose there are $$ N $$ high schools in the city and we want to study a manageable number, say $$ k $$ schools. List all high schools and randomly select $$ k $$ schools using a random number generator or random digit table.

3. **Collect Data Within Clusters:**  
   Once the $$ k $$ schools are chosen, include all students (or a complete random sample within each chosen school) from these schools. This helps capture the variability within selected clusters.

4. **Analysis:**  
   The sample now consists of students only from the selected high schools. Analyze their academic performance to draw inferences about the overall population of high school students.

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### Systematic Sampling

**Study Objective:**  
Assess customer satisfaction in a supermarket chain during a busy shopping period. The population is all customers visiting the supermarket, and the characteristic of interest is the level of satisfaction with the shopping experience.

**Sampling Process:**  
1. **Determine the Sampling Interval:**  
   Suppose you expect about $$ N $$ customers over a certain period and you want a sample of $$ n $$ customers. The sampling interval is calculated as  
   $$
   k = \frac{N}{n}.
   $$

2. **Random Start:**  
   Choose a random starting number between $$ 1 $$ and $$ k $$. This randomness ensures that every customer has an equal chance of being selected.

3. **Select Every $$ k^{\text{th}} $$ Customer:**  
   Starting from the selected random start, select every $$ k^{\text{th}} $$ customer. For example, if the random start is $$ r $$, then the selected customers would be the $$ r^{\text{th}} $$, $$(r+k)^{\text{th}}$$, $$(r+2k)^{\text{th}}$$, and so on until the shopping period ends.

4. **Data Collection:**  
   Administer a customer satisfaction survey to each selected customer during or after their shopping experience. This provides a systematic sample to estimate the overall satisfaction of all supermarket customers.

5. **Analysis:**  
   Analyze the survey responses to draw inferences about customer satisfaction in the supermarket chain.

### Cluster Sampling **Study Objective:** Investigate the academic performance of high school students in a large city. The population includes all high school students, and the characteristic of interest is their overall academic performance (e.g., average test scores). **Sampling Process:** 1. **Divide the City into Clusters:** The city is divided into high schools, with each school representing a cluster. 2. **Randomly Select Clusters:** Use a random number generator to select a certain number of high schools from the list. 3. **Sample All Students in Selected Schools:** Include all students from the chosen high schools in the sample. 4. **Data Collection and Analysis:** Collect academic performance data from the sampled students to assess the overall academic performance of high school students in the city. --- ### Systematic Sampling **Study Objective:** Assess customer satisfaction in a supermarket chain during a busy shopping period. The population consists of all customers visiting the supermarket, and the characteristic of interest is the level of satisfaction with the shopping experience. **Sampling Process:** 1. **Determine the Sampling Interval:** Calculate the number of customers expected over a period and decide on the sample size. The sampling interval $$ k $$ is determined by dividing the total number of customers by the desired sample size. 2. **Random Start:** Choose a random starting point between 1 and $$ k $$. 3. **Select Every $$ k^{\text{th}} $$ Customer:** Starting from the random start, select every $$ k^{\text{th}} $$ customer during the shopping period. 4. **Data Collection:** Survey the selected customers about their satisfaction with the shopping experience. 5. **Analysis:** Analyze the survey responses to estimate the overall customer satisfaction in the supermarket chain.

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