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Sampling & Inference

Grade 11 · Statistics · Worksheet 1

  1. Olivia is studying smartphone usage patterns among high school students. She stands outside the school library and surveys every 5th student who enters. Out of 150 students surveyed, 120 own smartphones. The total school population is 750 students. Based on her sample, what is the estimated number of smartphone owners in the entire school? Answer: ______________
  2. Liam is conducting a survey about high school students' study habits. He stands outside the school library and asks every 5th student who enters about their study time. Out of 1000 students at the school, he surveys 40 students. What percentage of the total student population did Liam survey? Answer: ______________
  3. Olivia is conducting a survey about high school students' screen time habits. She stands outside the school library and asks every 5th student who enters to complete her survey. Out of 850 students at the school, she collects 85 responses. What percentage of the student population is represented in Olivia's sample? Answer: ______________
  4. Aroha is conducting a survey about student opinions on school start times. She stands outside the school library at 3:00 PM and asks every 5th student who leaves whether they think school should start later. Out of the 75 students she surveys, 57 say yes. The school principal claims this shows strong support for later start times, but Aroha worries about sampling bias. If there are 1,125 students total at the school, what percentage of the student population did Aroha actually survey? Answer: ______________
  5. Aroha is conducting a survey about high school students' study habits. She stands outside the school library and surveys every 10th student who enters. Out of 150 students surveyed, 112 reported studying more than 15 hours per week. If the school has 1200 students total, how many students would Aroha estimate study more than 15 hours per week? Answer: ______________
  6. Liam is conducting a survey about smartphone usage patterns by randomly selecting 200 students from his high school's football team roster of 800 students. The school has a total enrollment of 2000 students. What percentage of the total student population does Liam's sample represent? Answer: ______________
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Answer Key & Explanations

Sampling & Inference · Grade 11 · Worksheet 1

  1. Olivia is studying smartphone usage patterns among high school students. She stands outside the school library and surveys every 5th student who enters. Out of 150 students surveyed, 120 own smartphones. The total school population is 750 students. Based on her sample, what is the estimated number of smartphone owners in the entire school? Answer: 600 Solution: Calculate the proportion of smartphone owners in the sample: 120 smartphone owners ÷ 150 surveyed students = 0.8 Convert the proportion to a percentage: 0.8 × 100 = 80% Apply this percentage to the total school population: 80% of 750 students = 0.8 × 750 Calculate the estimated number: 0.8 × 750…
    Full step-by-step solution

    Step 1: Calculate the proportion of smartphone owners in the sample: 120 smartphone owners ÷ 150 surveyed students = 0.8 Step 2: Convert the proportion to a percentage: 0.8 × 100 = 80% Step 3: Apply this percentage to the total school population: 80% of 750 students = 0.8 × 750 Step 4: Calculate the estimated number: 0.8 × 750 = 600 The estimated number of smartphone owners in the entire school is 600.

  2. Liam is conducting a survey about high school students' study habits. He stands outside the school library and asks every 5th student who enters about their study time. Out of 1000 students at the school, he surveys 40 students. What percentage of the total student population did Liam survey? Answer: 4 Solution: Liam surveyed 40 students out of a total population of 1000 students.
    Full step-by-step solution

    Step 1: Liam surveyed 40 students out of a total population of 1000 students. Step 2: To find the percentage, divide the number surveyed by the total population: 40 ÷ 1000 = 0.04 Step 3: Convert the decimal to a percentage by multiplying by 100: 0.04 × 100 = 4% The answer is 4.

  3. Olivia is conducting a survey about high school students' screen time habits. She stands outside the school library and asks every 5th student who enters to complete her survey. Out of 850 students at the school, she collects 85 responses. What percentage of the student population is represented in Olivia's sample? Answer: 10 Solution: Identify the total population size: 850 students Identify the sample size collected: 85 responses Calculate the percentage: (sample size ÷ total population) × 100 (85 ÷ 850) × 100 = 0.1 × 100 = 10% The answer is 10.
    Full step-by-step solution

    Step 1: Identify the total population size: 850 students Step 2: Identify the sample size collected: 85 responses Step 3: Calculate the percentage: (sample size ÷ total population) × 100 Step 4: (85 ÷ 850) × 100 = 0.1 × 100 = 10% The answer is 10.

  4. Aroha is conducting a survey about student opinions on school start times. She stands outside the school library at 3:00 PM and asks every 5th student who leaves whether they think school should start later. Out of the 75 students she surveys, 57 say yes. The school principal claims this shows strong support for later start times, but Aroha worries about sampling bias. If there are 1,125 students total at the school, what percentage of the student population did Aroha actually survey? Answer: 6.67 Solution: Sample size = 75 students Population size = 1,125 students Calculate the percentage of the population surveyed Percentage = (Sample size / Population size) × 100 Percentage = (75 / 1,125) × 100 75 ÷ 1,125 = 0.066666...
    Full step-by-step solution

    Step 1: Identify the sample size and population size Sample size = 75 students Population size = 1,125 students Step 2: Calculate the percentage of the population surveyed Percentage = (Sample size / Population size) × 100 Percentage = (75 / 1,125) × 100 Step 3: Perform the division 75 ÷ 1,125 = 0.066666... Step 4: Convert to percentage 0.066666... × 100 = 6.6666...% Step 5: Round to two decimal places 6.6666...% rounds to 6.67% The answer is 6.67.

  5. Aroha is conducting a survey about high school students' study habits. She stands outside the school library and surveys every 10th student who enters. Out of 150 students surveyed, 112 reported studying more than 15 hours per week. If the school has 1200 students total, how many students would Aroha estimate study more than 15 hours per week? Answer: 896 Solution: Calculate the proportion of students in the sample who study more than 15 hours per week: 112/150 = 0.7467 Multiply this proportion by the total number of students in the school: 0.7467 × 1200 = 896 Round to the nearest whole number since we're estimating students: 896 The answer is 896.
    Full step-by-step solution

    Step 1: Calculate the proportion of students in the sample who study more than 15 hours per week: 112/150 = 0.7467 Step 2: Multiply this proportion by the total number of students in the school: 0.7467 × 1200 = 896 Step 3: Round to the nearest whole number since we're estimating students: 896 The answer is 896.

  6. Liam is conducting a survey about smartphone usage patterns by randomly selecting 200 students from his high school's football team roster of 800 students. The school has a total enrollment of 2000 students. What percentage of the total student population does Liam's sample represent? Answer: 10 Solution: Identify the sample size: 200 students Identify the total population: 2000 students Calculate the percentage: (200 ÷ 2000) × 100 200 ÷ 2000 = 0.10 0.10 × 100 = 10 The answer is 10.
    Full step-by-step solution

    Step 1: Identify the sample size: 200 students Step 2: Identify the total population: 2000 students Step 3: Calculate the percentage: (200 ÷ 2000) × 100 Step 4: 200 ÷ 2000 = 0.10 Step 5: 0.10 × 100 = 10 The answer is 10.