Question 1: A school has 300 students: 150 boys and 150 girls. If a researcher wants a sample of 30 students using stratified sampling, how many boys and girls should be in the sample?

Answer: 15 boys and 15 girls

Question 2: Calculate the sample size for each stratum if a population of 800 students (600 in Year 9, 200 in Year 10) is to be sampled with a total of 80 students.

Answer: Year 9: 60, Year 10: 20

Question 3: If a stratified sample gave 40 students from a population of 500, with 300 in Stratum A and 200 in Stratum B, how many students should be sampled from each stratum?

Answer: Stratum A: 24, Stratum B: 16

Question 4: Identify the mistake in this stratified sampling approach: A researcher samples 10% from each stratum without considering the total population size.

Answer: The mistake is assuming the same proportional sampling from each stratum without adjusting for different population sizes or total sample size. Stratified sampling requires proportional allocation based on each stratum's size relative to the population.

Question 5: A survey divides a population of 1,200 students into three strata: Year 9 (400 students), Year 10 (500 students), Year 11 (300 students). To get a sample of 120 students, how many should be sampled from each year?

Answer: Year 9: 40, Year 10: 50, Year 11: 30

Question 6: Construct a stratified sample from a population of 600 with 200 in each of three strata, aiming for a total sample of 60. How many from each stratum?

Answer: Each stratum: 20

Question 7: Explain why stratified sampling can produce more accurate results than simple random sampling in a heterogeneous population.

Answer: Because stratified sampling ensures representation from each subgroup, reducing bias and variability, leading to more precise estimates of the whole population.

Question 8: A teacher wants to sample students from two classes, each with 50 students, to get a total of 20 students. How many should be sampled from each class?

Answer: 10 from each class

Question 9: A population of 1,000 students is divided into three strata: 300 in Stratum 1, 400 in Stratum 2, and 300 in Stratum 3. If 150 students are sampled, how many should come from each stratum?

Answer: Stratum 1: 45, Stratum 2: 60, Stratum 3: 45

Question 10: Identify a common error in proportional stratified sampling and suggest a correction.

Answer: A common error is using the same proportion for all strata without considering their actual sizes or the total sample size. Correction: Calculate the sample size for each stratum using the formula: (Stratum size / Total population) × Total sample size.

Question 11: A stratified random sample of 90 students is taken from a population of 900 students divided equally into three strata. How many students are sampled from each stratum?

Answer: 30 students from each stratum