Question 1: A school has 300 students. To conduct a survey, 30 students are selected at random. Explain why this method is an example of random sampling.

Answer: Because each student has an equal chance of being selected, ensuring unbiased representation.

Question 2: Calculate the sampling fraction when 45 students are chosen from a population of 900.

Answer: 0.05

Question 3: Identify the mistake in the following sampling method: 'Selecting every 10th student from a list, starting at a random point.'

Answer: This is systematic sampling, which is not purely random because it depends on the starting point.

Question 4: A researcher claims that choosing 10% of a population at random always gives a representative sample. Is this statement true? Explain your answer.

Answer: Not necessarily; a small or biased sample can still be unrepresentative despite being random.

Question 5: Construct a simple random sample of 5 students from a class of 20, using the grid provided. (Describe the process.)

Answer: Assign numbers 1-20 to students and randomly select five numbers using a random number generator or table.

Question 6: A survey was conducted by selecting students from only one side of the school. Identify the error or misconception in this sampling approach.

Answer: The sample is biased because it does not represent the entire student population.

Question 7: Explain how increasing the sample size affects the reliability of the results, assuming the sampling method remains random.

Answer: Increasing the sample size generally improves reliability and reduces sampling error.

Question 8: A class of 40 students is divided into 4 groups of 10. A teacher randomly selects one entire group to survey. Is this an example of simple random sampling? Why or why not?

Answer: No, because selecting an entire group is cluster sampling, not simple random sampling.

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

Answer: Students will plot points (0,0), (1,2), (2,4), ..., (10,20).

Question 10: A sample of 50 people is taken from a population of 200. The sample yields 35% support for a new policy. Calculate the margin of error if the confidence level is 95%. (Use approximate formula: margin of error ≈ 1.96 * sqrt(p(1-p)/n)).

Answer: Approximately ± 8.2%

Question 11: A common error in random sampling is to assume that a larger sample always leads to better accuracy. Identify and explain this misconception.

Answer: Larger samples reduce error, but if the sampling method is biased, accuracy does not necessarily improve.

Question 12: In a survey, students believe that choosing only students who volunteer is a good way to get a representative sample. Why is this a misconception?

Answer: Because volunteers may have different opinions from the general population, leading to biased results.