Statistical Bias and Sampling Worksheets Grade 10

1. Aroha wants to estimate the average height of all students at her school. She stands outside the gymnasium after a basketball game and asks every 5th student who exits to measure their height. Identify the sampling method used, the type of bias present, and explain why this sample may not represent the entire school population.
2. Hana is a school board member investigating whether the new school library hours meet the needs of all students at a large high school. She places a survey on the library's front desk for one week and asks students to fill it out voluntarily as they visit the library. A total of 120 students complete the survey, and 96 of them say the hours are sufficient. However, the school has 800 students total. Identify and explain two distinct types of bias present in Hana's sampling method, and state why the results cannot be generalized to the entire student population.
3. Charlotte wants to estimate the average height of students at her school. She stands outside the gymnasium after a basketball game and surveys the first 40 students who exit. Identify the type of sampling bias present in this method and explain why it leads to a biased estimate.

…and 2 more problems

1. Liam wants to estimate the average height of students at his school. He surveys 50 students from the basketball team. Identify the type of sampling bias present and explain why this sample is not representative of the entire student population.
2. Mere wants to estimate the average height of all students at her school. She posts a survey on the school's social media page and asks students to voluntarily submit their height. Of the 1200 students at the school, only 84 respond. Identify the sampling method used, the type of bias present, and explain why this bias is problematic.
3. A city council wants to estimate the average daily screen time for teenagers in their city. The city has 15,000 teenagers aged 13-18. The council surveys the first 80 students who enter the public library on Saturday morning. If the true population mean is 6.2 hours per day with a standard deviation of 1.8 hours, what is the approximate standard error of the mean for this sampling method?

…and 2 more problems

1. A triangular prism has a right triangle base with legs measuring 6 cm and 8 cm, and a height of 15 cm. The prism is sliced by a plane that passes through the midpoint of the prism's height and is parallel to the triangular bases. What is the area of the cross-section formed by this slice?
2. A university is studying the average study time per week for undergraduate students. They randomly select 500 students from their enrollment database, but only 180 students respond to the survey. The respondents have an average study time of 18 hours per week, while the non-respondents are later found to average only 8 hours per week. Calculate the actual average study time for all 500 selected students, accounting for non-response bias.
3. Olivia wants to estimate the average number of hours students at her school spend on homework per week. She posts a survey link on the school's social media page and receives responses from 75 students. Identify the sampling method used, the type of bias present, and explain why this method may lead to an inaccurate estimate.

…and 3 more problems