Question 1: Stratified sampling involves dividing a population into distinct subgroups called strata, then randomly sampling from each stratum proportionally. The key formula for the sample size from each stratum is: (Size of stratum / Total population) * Total sample size.

Answer: See explanation

Question 1: A school has 300 students, with 150 boys and 150 girls. If a researcher wants to select a total sample of 60 students using stratified sampling, how many boys and girls should be sampled?

Answer: Boys: 30, Girls: 30

Question 2: In a city, 40% of residents are under 18, and 60% are 18 or older. If 120 residents are sampled proportionally, how many are under 18?

Answer: 48

Question 3: Explain why proportional sampling from each stratum is important in stratified sampling.

Answer: It ensures the sample accurately reflects the population structure.

Question 1: A university has 10,000 students: 6,000 undergraduates and 4,000 postgraduates. To survey 500 students, how many should be sampled from each group using stratified sampling? Show your working.

Answer: Undergraduates: 300, Postgraduates: 200

Question 2: A researcher notices that in their stratified sample, the number of students sampled from each stratum does not match the proportions in the population. What effect could this have on the results? Provide an explanation.

Answer: It could bias the results and not accurately represent the population.

Question 3: Identify a common mistake when selecting samples from strata and explain how to avoid it.

Answer: Choosing equal numbers from each stratum regardless of their proportion; avoid by calculating sample sizes proportionally.

Question 1: A company wants to survey customer satisfaction across four regions: North, South, East, West. The regions have the following customer populations: North - 5000, South - 3000, East - 2000, West - 1000. If they plan to survey 400 customers, how many should be sampled from each region?

Answer: North: 200, South: 120, East: 80, West: 40

Question 2: A school believes that a simple random sample does not accurately represent the diversity of its student body. How can stratified sampling improve the accuracy of their survey?

Answer: It ensures representation from all subgroups, reflecting the population's diversity.

Question 1: Design a stratified sampling plan for a survey of a city where demographic data shows 25% children, 50% adults, and 25% seniors. If the total sample size is 200, how many should be taken from each group? Explain your reasoning.

Answer: Children: 50, Adults: 100, Seniors: 50

Question 2: Suppose a stratified sample has unequal numbers from each stratum due to sampling errors. How might this impact the validity of conclusions drawn from the survey? Provide a detailed explanation.

Answer: It can bias results, over-represent some groups, and lead to incorrect generalizations.

Question 1: A researcher mistakenly sampled 20 students from each stratum regardless of the population size. Identify the mistake and explain its potential effect on the results.

Answer: The mistake is not sampling proportionally; it may bias the results and misrepresent the population.

Question 2: A student claims that stratified sampling is unnecessary if the population is homogeneous. Is this correct? Justify your answer.

Answer: Incorrect; stratified sampling is unnecessary if the population is homogeneous because simple random sampling suffices.