Question 1: A class of 30 students is to be selected randomly for a survey. If 6 students are chosen at random, what is the probability that a specific student is included in the sample?

Answer: 1/5

Question 2: Calculate the expected number of males in a random sample of 50 students, given that 60% of the entire school population are males.

Answer: 30

Question 3: Explain why simple random sampling ensures every individual has an equal chance of selection. Provide one advantage of this method over convenience sampling.

Answer: Simple random sampling assigns each individual an equal probability, reducing bias and ensuring representativeness.

Question 4: Construct a random sample of 4 numbers from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Show your method.

Answer: Use a random number generator or draw numbers from a hat; for example, 2, 7, 4, 9.

Question 5: A researcher randomly selects 100 samples from a population of 10,000. What is the probability that a particular individual is included in the sample?

Answer: 0.01

Question 6: If a sample of 20 students is randomly selected from a school of 200 students, what is the probability that exactly 3 females are chosen, assuming 50% of the students are female? (Use binomial approximation)

Answer: Approx. 0.180

Question 7: Identify and explain one common mistake when sampling randomly from a list that is not well-shuffled.

Answer: Selecting from the top of a list may introduce bias; proper shuffling ensures each individual has an equal chance.

Question 8: A survey of 150 people randomly sampled from a city reports that 45% prefer tea over coffee. What is the margin of error at a 95% confidence level?

Answer: Approximately 0.098

Question 9: A company wants to estimate the average number of emails its employees receive daily. They take a random sample of 40 employees and find the mean is 15 emails with a standard deviation of 4. Construct a 95% confidence interval for the true average.

Answer: [13.4, 16.6]

Question 10: In a class of 35 students, a teacher randomly assigns students to two groups for an experiment. Explain why random sampling might be important in selecting participants and how it affects the validity of results.

Answer: Random sampling reduces selection bias, ensuring groups are comparable and findings are more generalizable.

Question 11: A researcher mistakenly samples only from the morning shift employees, believing they are representative of all employees. Identify the error and suggest a correction.

Answer: The mistake is sampling from only one shift, which introduces bias. The correction is to sample across all shifts.

Question 12: A study claims a 95% confidence level with a margin of error of ±3%. If the sample size was increased, what would happen to the margin of error? Explain briefly.

Answer: It would decrease, improving estimate precision, because larger samples reduce variability.