Question 1: Define bias in the context of sampling in your own words.

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

Question 2: A survey samples students by only asking those in the school cafeteria during lunch. Is this an example of biased sampling? Why or why not?

Answer: Yes, it is biased because only students who eat in the cafeteria during lunch are sampled, excluding students who do not eat there or are absent.

Question 3: Calculate the bias percentage if a survey claims 80% support a new school rule, but the actual support in the entire student body is 70%.

Answer: Bias = (Observed - True) / True * 100 = (80 - 70) / 70 * 100 = 14.29%

Question 4: Construct a simple diagram on the grid to represent an unbiased random sampling method, such as drawing names from a hat.

Answer: Students draw names randomly from a hat, ensuring each has an equal chance.

Question 5: Explain why convenience sampling can introduce bias into a survey.

Answer: Convenience sampling selects easily accessible individuals, which may not represent the entire population, leading to biased results.

Question 6: In a class of 30 students, a teacher surveys the first 10 students who arrive. Is this likely to be biased? Why?

Answer: Yes, because early arrivals may have different characteristics, such as more punctuality, which may bias the results.

Question 7: If a sample overrepresents a particular subgroup, how does this affect the overall data? Provide a brief explanation.

Answer: It skews the results, making the data unrepresentative of the entire population and possibly leading to incorrect conclusions.

Question 8: A survey asks only students who are wearing sports uniforms about participation in sports. Is this biased? Why?

Answer: Yes, because students in sports uniforms are more likely to participate in sports, so the sample overstates actual participation.

Question 9: Calculate the bias if a sample reports 60% support for a new policy, but the true support is 50%.

Answer: Bias = (60 - 50) / 50 * 100 = 20%

Question 10: Identify one method to reduce bias in a sampling process and explain briefly.

Answer: Use random sampling where every individual has an equal chance of being selected, reducing systematic bias.

Question 11: A researcher finds that the sample overestimates the average height of students. What might be a cause of this bias?

Answer: The sample may have included more taller students, perhaps due to sampling only from a sports team or group of athletes.

Question 12: Identify and correct the mistake in this statement: 'Sampling only from the evening class will give an unbiased estimate of the entire student population.'

Answer: This is biased because the evening class may differ from other classes, so it does not represent the entire student population.