Question 1: Define bias in the context of sampling and explain why it can lead to inaccurate results.

Answer: Bias in sampling is a systematic error that causes the sample to not accurately represent the population, leading to distorted results.

Question 2: Identify which of the following sampling methods is most likely to introduce bias: A) Random sampling, B) Stratified sampling, C) Convenience sampling, D) Systematic sampling.

Answer: C

Question 3: A survey is conducted in a supermarket where only shoppers in the checkout queue are asked about their shopping habits. Explain how this sampling method could be biased.

Answer: This method may be biased because it only samples shoppers at checkout, who may not be representative of all shoppers (e.g., those shopping quickly or with fewer items).

Question 4: Calculate the percentage bias if a survey over-represents a particular age group by 20% compared to the actual population proportion.

Answer: 20%

Question 5: List two common sources of bias in sampling and briefly describe how each can affect results.

Answer: Selection bias (non-representative sample) and response bias (misleading answers), both can distort the true picture of the population.

Question 6: A school surveys students' preferred lunch options by only asking those in the school cafeteria during lunch hour. Does this method risk bias? Explain.

Answer: Yes, because students not in the cafeteria during lunch may have different preferences, leading to unrepresentative results.

Question 7: Construct a simple diagram on the grid to illustrate how bias might occur if a survey only includes people with certain characteristics.

Answer: Students draw a diagram showing a biased sample area within a larger population area, highlighting how certain groups are overrepresented.

Question 8: A researcher notices that their sample has more males than females, unlike the actual population. What kind of bias is this? How might it affect the results?

Answer: This is sampling bias; it can lead to results that do not accurately reflect the overall population's characteristics.

Question 9: Explain why voluntary response samples are often biased.

Answer: Because only those with strong opinions choose to respond, leading to overrepresentation of extreme views and a non-representative sample.

Question 10: A poll shows that 80% of respondents favor a new policy, but only 10% of the population responded. Why might this result be biased?

Answer: Because only a small, possibly motivated segment responded, it may not reflect the views of the entire population, leading to response bias.

Question 11: Identify and correct the bias in this scenario: A survey about exercise habits is conducted only on gym members.

Answer: The bias is sampling bias. To correct it, include a random sample of the general population, not just gym members.