Question 1: Calculate the probability of selecting a female student from a class of 30 students, where 18 are female, using a random sampling method.

Answer: 3/5

Question 2: In a city, a surveyor randomly samples 50 households out of 500 to estimate the average household income. If the sample mean income is £30,000, what is the estimated total income of all households?

Answer: £15,000,000

Question 3: A factory samples 200 products out of a batch of 10,000 to check for defects. If 3% of the sample are defective, estimate the total number of defective products in the batch.

Answer: 300

Question 4: Explain why random sampling is important when collecting data for a survey about student preferences for school activities.

Answer: Random sampling ensures that every student has an equal chance of being selected, minimizing bias and making the results representative of the entire student population.

Question 5: A researcher randomly selects 60 individuals from a population of 600. The sample includes 24 males and 36 females. What is the proportion of males in the sample?

Answer: 0.4

Question 6: Construct a simple random sample of 10 students from a class of 40 using a numbered list. Describe the process.

Answer: Number all students from 1 to 40, then randomly select 10 numbers using a random number generator or lottery method to form the sample.

Question 7: A survey of 150 customers finds that 45 prefer product A. If this sample is randomly selected from a population of 1500 customers, estimate how many customers prefer product A in the entire population.

Answer: 450

Question 8: Identify and correct the mistake in the following statement: 'A researcher surveys 20 students from a school of 300 students, choosing the first 20 students they meet.'

Answer: The sample is biased because it only includes students the researcher meets first; for random sampling, students should be chosen randomly from the entire school list.

Question 9: Plot the graph of y = 2x for x values from 0 to 10 on the grid. Draw the line clearly.

Answer: Student draws the line passing through points (0,0), (1,2), (2,4), ... (10,20).

Question 10: A company randomly samples 100 products from a batch of 500 to check for quality. They find 5 defective items. How many defective items are estimated in the whole batch?

Answer: 10

Question 11: A school wants to estimate the average number of hours students spend on homework per week. They survey 40 students chosen randomly from 400 students. The sample average is 8 hours. What is the total estimated hours spent by all students?

Answer: 3,200 hours

Question 12: Challenge question: Explain how stratified sampling could improve the accuracy of a survey about student preferences across different year groups in a school.

Answer: Stratified sampling divides the population into subgroups (strata), such as year groups, and samples from each proportionally. This ensures representation from all groups, reducing sampling bias and improving accuracy compared to simple random sampling.