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

Answer: Bias in sampling occurs when certain members of a population are more likely to be included than others, leading to unrepresentative samples and potentially inaccurate results.

Question 2: Calculate the bias percentage if a survey aimed at 200 people only includes students from a single school that has 500 students in total.

Answer: Bias percentage = ((Number of surveyed students / Total students) - 1) × 100 = ((200/500) - 1) × 100 = (-0.6) × 100 = -60%

Question 3: Describe a real-world scenario where sampling bias might occur and how it could affect the results.

Answer: If a company only surveys customers who visit during weekdays, the feedback may be biased as it excludes those who shop on weekends, leading to unrepresentative customer opinions.

Question 4: Identify the type of bias in this sample: A researcher surveys only tall people to study average height.

Answer: Selection bias or sampling bias

Question 5: Construct a simple random sample of size 10 from a population of 50 students numbered 1 to 50. Use the grid to select the sample.

Answer: Students numbered 7, 14, 23, 27, 33, 41, 45, 48, 3, 12 (example; actual answer depends on random selection).

Question 6: A survey about favorite sports is conducted only among members of a local sports club. What type of bias might this introduce?

Answer: Sampling bias, because the sample is not representative of the general population.

Question 7: Explain how non-response bias can affect survey results and suggest a way to minimize it.

Answer: Non-response bias occurs when certain groups do not respond, skewing results. To reduce it, follow up with non-respondents and ensure anonymity to encourage participation.

Question 8: Given the data: 150 students were surveyed, but only 50 responses were received. The survey was distributed to 300 students in total. Calculate the response rate and discuss how this might introduce bias.

Answer: Response rate = (50 / 150) × 100 = 33.33%. Low response rate can cause non-response bias, as the opinions of non-respondents might differ from respondents.

Question 9: Propose a method to reduce selection bias when conducting a survey in a large city.

Answer: Use stratified random sampling to ensure all subgroups (e.g., age, income, location) are proportionately represented in the sample.

Question 10: Identify and correct the bias: A study only includes data from online surveys posted on social media, excluding those without internet access.

Answer: This introduces selection bias; to correct it, include offline data collection methods to reach those without internet access.

Question 11: A researcher notices that their sample overrepresents males compared to the overall population. What bias is this, and how can it be addressed?

Answer: This is gender bias; it can be addressed by ensuring the sampling method includes an equal or representative number of males and females.