Question 1: Explain in your own words what stratified sampling is and why it might be used instead of simple random sampling.

Answer: Stratified sampling involves dividing a population into subgroups (strata) based on specific characteristics, then sampling from each subgroup proportionally. It is used to ensure representation of all subgroups and improve accuracy.

Question 2: Calculate the number of students to sample from each grade if there are 300 students in total, with 100 in 7th grade, 120 in 8th, and 80 in 9th, and you need a sample of 60 students.

Answer: 7th grade: 20, 8th grade: 24, 9th grade: 16

Question 3: If the population of a school has 50 boys and 50 girls, how many boys and girls should be sampled to maintain proportional representation in a sample of 20 students?

Answer: Boys: 10, Girls: 10

Question 4: Construct a simple example of stratified sampling using two strata: 'urban' and 'rural' populations, with 60 urban and 40 rural people. Show how you would select a proportional sample of 10 people.

Answer: Urban: 6, Rural: 4

Question 5: A class has 15 boys and 10 girls. If a stratified sample of 8 students is taken proportionally, how many boys and girls are sampled?

Answer: Boys: 4, Girls: 3

Question 6: A survey wants to sample 50 students from a school with 200 students divided into 4 classes of 50 students each. How many students should be sampled from each class?

Answer: 12 or 13 students from each class

Question 7: In a population consisting of 40% category A and 60% category B, how would you determine the number of samples from each category if the total sample size is 100?

Answer: Category A: 40, Category B: 60

Question 8: A researcher samples 20 students from two classes: Class 1 has 80 students, and Class 2 has 120 students. How many students should be sampled from each class to maintain proportionality?

Answer: Class 1: 10, Class 2: 10

Question 9: Identify a common mistake students might make when calculating stratified samples and explain how to avoid it.

Answer: Mistake: Not maintaining proportionality when selecting samples. To avoid it, always calculate the proportion of each subgroup and multiply by the total sample size.

Question 10: Given the following data, calculate the stratified sample: A city has 30% of its population in District A and 70% in District B. If 90 people are to be sampled, how many from each district?

Answer: District A: 27, District B: 63

Question 11: A school is divided into three clubs: Drama, Music, and Sports, with 40, 30, and 30 members respectively. How would you select a stratified sample of 15 students?

Answer: Drama: 6, Music: 5, Sports: 4