By the end of this chapter, you will be able to:
Mastering these skills will help you gather trustworthy data, making your research more effective and valuable in your trade.
In applied statistics, designing an effective sampling strategy is crucial for any research or data-driven decision-making process. Applied statisticians in Kenya often face challenges such as limited resources, diverse populations, and the need for reliable and actionable insights. Understanding how to identify the target population and develop a robust sampling design ensures that collected data accurately represents the group of interest. This chapter provides a practical mathematical foundation for identifying populations and samples, then constructing appropriate sampling frames and designs for real-world applied statistics work.
A target population is the entire set of individuals or units about which information is required. In practice, statisticians rarely study entire populations due to constraints of time, cost, and logistics. Instead, they select a sample that is representative of the population, allowing them to make valid inferences.
In statistics, a population refers to all individuals, items, or data points with a common characteristic that is the subject of a study. Populations can be finite or infinite, and are defined by the research objectives.
Example 1: A county government wants to know the average household income in Kisumu County. If there are 250,000 households, what is the size of the population?
Given:
Number of households in Kisumu County = 250,000
Population size, \( N = 250,000 \)
Answer: \( N = 250,000 \) households
Example 2: A bank wants to determine the default rate among all its 12,000 loan accounts. What is the population?
Given:
Number of loan accounts = 12,000
Population size, \( N = 12,000 \)
Answer: \( N = 12,000 \) loan accounts
Example 3: A university is conducting a study on exam performance among all first-year students. If there are 3,800 first-year students, what is the population?
Given:
Number of first-year students = 3,800
Population size, \( N = 3,800 \)
Answer: \( N = 3,800 \) students
Example 4: A SACCO wants to survey all its members about a new product. If the SACCO has 7,500 members, what is the population?
Given:
Number of SACCO members = 7,500
Population size, \( N = 7,500 \)
Answer: \( N = 7,500 \) members
Example 5: A farm cooperative is studying milk yields from all its 1,200 cows. What is the target population?
Given:
Number of cows = 1,200
Population size, \( N = 1,200 \)
Answer: \( N = 1,200 \) cows
A sample is a subset of the population selected for analysis, with the aim of drawing conclusions about the entire population. Sampling is essential when it is impractical or impossible to collect data from every member of the population.
Example 1: From a population of 2,000 secondary school teachers in Nairobi, a statistician selects 100 teachers for a survey. What is the sample size?
Given:
Population size, \( N = 2,000 \)
Sample size, \( n = 100 \)
Answer: \( n = 100 \) teachers
Example 2: A retail chain has 400 shops. To estimate average monthly sales, it randomly selects 40 shops. What is the sample size?
Given:
Population size, \( N = 400 \)
Sample size, \( n = 40 \)
Answer: \( n = 40 \) shops
Example 3: A survey on maize yield is conducted in a county with 15,000 farms. Data is collected from 500 randomly selected farms. What is the sample size?
Given:
Population size, \( N = 15,000 \)
Sample size, \( n = 500 \)
Answer: \( n = 500 \) farms
Example 4: Out of 10,000 registered nurses in Kenya, a researcher selects 250 for a health study. What is the sample size?
Given:
Population size, \( N = 10,000 \)
Sample size, \( n = 250 \)
Answer: \( n = 250 \) nurses
Example 5: In a survey on youth unemployment, 120 out of 2,500 job seekers are interviewed. What is the sample size?
Given:
Population size, \( N = 2,500 \)
Sample size, \( n = 120 \)
Answer: \( n = 120 \) job seekers
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Create a free accountThis chapter provided an overview of essential statistical procedures for sampling in research. It began by distinguishing between the target population and the sample, clarifying their roles in research design. The concept of sampling design and frame was introduced, emphasizing the importance of structuring how samples are selected. Various sampling and sampling techniques were discussed, outlining methods to ensure representative and unbiased selection. The chapter then explored sample size determination, presenting calculation methods for both means and proportions to achieve reliable results. Finally, the development of data collection tools was examined, highlighting their role in gathering accurate and relevant information from the chosen sample. Together, these topics equip learners with the foundational skills to design effective sampling strategies for research projects.
Given:
Population \( N = 2{,}000 \)
Sample size \( n = 100 \)
Sample mean \( \bar{x} = 310 \) litres
Sample standard deviation \( s = 40 \) litres
Formula:
Standard error of the mean:$$
SE = \frac{s}{\sqrt{n}}
$$
Substitution:$$ SE = \frac{40}{\sqrt{100}} $$
Computation:$$ \sqrt{100} = 10 $$$$ SE = \frac{40}{10} $$$$ SE = 4 $$
Final Answer:
\(\boxed{4\ \text{litres}}\)
Given:
Population \( N = 500 \)
Sample size \( n = 25 \)
Formula:
Sampling interval$$
k = \frac{N}{n}
$$
Substitution:$$ k = \frac{500}{25} $$
Computation:$$ k = 20 $$
Final Answer:
\(\boxed{20}\)
The Kenya National Bureau of Statistics (KNBS) is planning to conduct a survey on maize production in Uasin Gishu County. Define the target population for this study and explain why it is important to accurately identify the target population. (4 marks)
Distinguish between a population and a sample in applied statistics and give an example relevant to water quality research in Lake Victoria. (4 marks)
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