Question 1: A population of 600 students is divided into 3 strata: Year 10 (200 students), Year 11 (250 students), and Year 12 (150 students). If a stratified sample of 60 students is to be taken proportionally, how many students should be sampled from each year?

Answer: Year 10: 20, Year 11: 25, Year 12: 15

Question 2: Calculate the proportion of students in each stratum and the corresponding number in a sample of 80 students.

Answer: Year 10: 0.333, 27; Year 11: 0.417, 33; Year 12: 0.25, 20

Question 3: Explain briefly why stratified sampling can give more accurate results than simple random sampling in a diverse population.

Answer: It ensures representation from all key subgroups, reducing sampling bias and improving accuracy.

Question 1: A school has 300 students, with 120 in year 10, 100 in year 11, and 80 in year 12. You want to select a stratified sample of 75 students proportional to each year group. How many students should be selected from each year? Justify your answer.

Answer: Year 10: 30, Year 11: 25, Year 12: 20

Question 2: A survey requires a sample of 120 people from a town with 40% males and 60% females. The population is divided into two districts: District A (60% of the population) and District B (40%). If you want proportional sampling within each district, how many males and females should be sampled from each district?

Answer: District A: Males 28.8, Females 41.6; District B: Males 16.8, Females 25.2

Question 3: Describe a real-world scenario where stratified sampling would be preferable over simple random sampling, and explain why.

Answer: In a national health survey, stratifying by age groups ensures each age group is properly represented, leading to more accurate health data across different demographics.

Question 4: A class has 30 students: 12 boys and 18 girls. You need to select a sample of 6 students proportionally. How many boys and girls should be in the sample?

Answer: Boys: 2, Girls: 4

Question 5: Why might a researcher choose to use stratified sampling instead of simple random sampling when studying customer satisfaction across different store branches?

Answer: To ensure each branch is adequately represented, providing more reliable comparisons between branches.

Question 1: Construct a stratified sampling plan for a university with 10,000 students divided into faculties: Science (4000), Arts (3000), Engineering (2000), and Business (1000). Sample 500 students proportionally, and show how many from each faculty.

Answer: Science: 200, Arts: 150, Engineering: 100, Business: 50

Question 2: A stratified sample of 200 employees is taken from a company with 600 employees: 300 in the marketing department and 300 in the sales department. Calculate the sample size from each department if proportional sampling is used.

Answer: Marketing: 100, Sales: 100

Question 3: Identify a common mistake students might make when calculating sample sizes proportionally across strata, and suggest how to avoid it.

Answer: Rounding errors leading to total samples not matching the intended size; avoid by adjusting the last stratum's count accordingly.

Question 1: A population of 15,000 is divided into 4 strata: A (5000), B (4000), C (3000), D (2000). If a sample of 600 is taken proportionally, but the proportion of a certain characteristic is known to differ across strata, how should the researcher adjust the sampling method to ensure accurate estimates?

Answer: Use stratified sampling with different sampling fractions in each stratum based on characteristic prevalence, not just proportion.

Question 2: Given the initial stratified sample sizes calculated, how would you handle a scenario where the sum of rounded sample sizes exceeds or is less than the total desired sample size? Provide a method to correct this.

Answer: Adjust the largest or last stratum's sample size to compensate for rounding discrepancies, ensuring total matches the target.

Question 1: A student calculates the sample size for each stratum but ignores rounding, resulting in a total sample size of 610 instead of 600. How should they correct this mistake?

Answer: Adjust one or more stratum sizes to ensure the total equals 600, typically by reducing the largest or last stratum's count.

Question 2: A student forgets to proportionally assign samples when the population is divided into multiple strata. Explain why this is an error and how to fix it.

Answer: It causes bias and unrepresentative samples; fix by calculating each stratum's proportion of the total population and sampling accordingly.