Question 1: A class has 30 students. A random sample of 5 students is selected. How many different samples can be formed?

Answer: 142506

Question 2: A surveyor randomly selects 10 houses from a neighborhood of 200 houses. What is the probability that a specific house is selected?

Answer: 1/20

Question 3: Explain why random sampling is important for reducing bias in surveys.

Answer: Random sampling ensures each individual has an equal chance of being selected, minimizing bias and making the sample more representative of the population.

Question 4: Construct a simple random sample of 4 numbers from the set {1, 2, 3, 4, 5, 6, 7, 8}. Explain your method.

Answer: Use a random number generator or draw numbers from a hat; for example, pick 2, 5, 7, 3.

Question 5: A company wants to survey 15 employees out of 150. If they select employees randomly, what is the probability that Employee A is chosen?

Answer: 15/150 = 1/10

Question 6: In a random sample of 50 people from a population of 1000, how many people would you expect to be over 50 years old if 20% of the population is over 50?

Answer: 10

Question 7: Plot the graph of y = 3x for x values from 0 to 5 on the grid.

Answer: Students will draw a straight line passing through (0,0), (1,3), (2,6), (3,9), (4,12), (5,15).

Question 8: A researcher selects a sample of 20 students from a school with 400 students. If the sampling is not random and every 20th student is chosen, what kind of bias might this introduce?

Answer: This could introduce systematic bias, as the sample may not be representative if there are patterns in student ordering.

Question 9: Identify a common mistake when calculating the probability that a specific individual is chosen in a simple random sample, and explain how to correct it.

Answer: A common mistake is to assume probability equals sample size divided by population size without considering sampling without replacement. To correct, recognize that the probability is 1 divided by the total population if sampling randomly and independently.

Question 10: A bag contains 8 red, 6 blue, and 6 green balls. If 5 balls are drawn at random without replacement, what is the probability that exactly 2 are red?

Answer: Combine combinations: (C(8,2) * C(14,3)) / C(20,5).

Question 11: A school conducts a survey by randomly selecting 25 students from a total of 500. If 60% of the students are boys, estimate how many boys are likely to be in the sample.

Answer: 15

Question 12: Explain a situation where random sampling might fail to produce a representative sample and suggest a way to improve it.

Answer: If the sampling frame is incomplete or biased (e.g., only accessible individuals), the sample may not be representative. To improve, ensure the sampling frame includes all relevant members and use stratified sampling if needed.