Question 1: Define stratified sampling and write the key formula used to calculate the sample size from each stratum.

Answer: Stratified sampling involves dividing a population into strata and sampling from each; formula: n_i = (N_i / N) * n

Question 2: Given a population of 300 students divided into 3 classes (100, 100, 100), how many students should be sampled from each class if a total sample size of 60 is needed, assuming proportional stratified sampling?

Answer: Class 1: 20, Class 2: 20, Class 3: 20

Question 3: In a population of 500, 200 are males and 300 are females. If a sample of 50 is taken using stratified sampling, how many males and females should be included?

Answer: Males: 20, Females: 30

Question 4: Explain why stratified sampling can provide more accurate results than simple random sampling in heterogeneous populations.

Answer: Because it ensures all subgroups are proportionally represented, reducing sampling bias and increasing precision.

Question 5: A school has 4 grade levels: Year 7 (150 students), Year 8 (130), Year 9 (120), Year 10 (100). If 40 students are randomly sampled proportionally from each grade, how many students are sampled from Year 8?

Answer: Year 8: 34

Question 6: Describe a real-world scenario where stratified sampling would be preferable over simple random sampling.

Answer: Surveying customer satisfaction across different store locations to ensure all locations are proportionally represented.

Question 7: Calculate the number of students to sample from each of three classes (Class A: 80 students, Class B: 60 students, Class C: 60 students) if a total of 50 students are to be sampled proportionally.

Answer: Class A: 20, Class B: 15, Class C: 15

Question 8: A researcher mistakenly samples 25% of each stratum regardless of their size, instead of proportionally. What potential mistake does this introduce?

Answer: It may lead to over-representation of smaller strata and under-representation of larger ones, biasing results.

Question 9: Construct a scenario where stratified sampling might fail or produce misleading results. Explain why.

Answer: If strata are not well-defined or the population is not properly divided, sampling may not represent the true diversity, leading to biased or misleading results.

Question 10: Identify and correct the mistake in this stratified sampling approach: 'Sampling 10 students from each of 5 classes, regardless of class size.'

Answer: The mistake is not sampling proportionally to class sizes; should adjust sample size for each class based on its population.