Question 1: Define bias in the context of sampling. Why is it important to minimize bias?

Answer: Bias is a systematic error that skews results, leading to unrepresentative samples. Minimizing bias ensures accurate, fair data collection.

Question 2: Calculate the percentage bias if a survey overestimates the number of respondents from a particular group by 15%.

Answer: 15%

Question 3: A school surveys 50 students but only from the morning classes. Explain how this sampling method might be biased.

Answer: Sampling only morning students introduces bias as it excludes students with different schedules, possibly affecting the representativeness of the survey.

Question 4: Construct a simple random sample of size 10 from a population of 50 students listed from 1 to 50.

Answer: Sample will vary; example: {3, 7, 12, 19, 23, 29, 34, 41, 45, 50}

Question 5: Identify two potential sources of bias in a phone survey where only landline numbers are used.

Answer: Excludes people without landlines and those who prefer mobile phones, leading to unrepresentative results.

Question 6: Explain how non-response bias can affect survey results and suggest one way to reduce it.

Answer: Non-response bias occurs when certain groups do not reply, skewing data. To reduce it, follow up with non-respondents or incentivize participation.

Question 7: A biased sample overestimates the true proportion of 'yes' responses by 10%. If the true proportion is 60%, what is the biased estimate?

Answer: 70%

Question 8: A researcher surveys only students in the top 10% of exam scores to infer the general student population's performance. What bias might this introduce?

Answer: Selection bias, as high-achieving students are not representative of all students, leading to an overestimation of average performance.

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

Answer: Student plots the line passing through (0,0) to (10,20).

Question 10: Identify and correct the bias in this survey statement: 'We only interviewed men aged 30-50 to determine people's opinions.'

Answer: The sample excludes women and other age groups, introducing gender and age bias. To correct, include a diverse sample.

Question 11: Discuss why convenience sampling often introduces bias and give an example.

Answer: Convenience sampling selects easily accessible individuals, which may not represent the entire population. Example: Surveying only passersby in a mall.

Question 12: A bias in data collection causes the estimated average height of a group to be 5 cm taller than the actual average. Calculate the bias percentage if the true average is 170 cm.

Answer: ~2.94%