7.10.6 Samples and Populations

Vocabulary Unbiased Sample: Random selection from a population that is large enough that the data is pretty accurate. example: Interviewing 90% of all the students in the school Biased Sample: Doesn’t represent the whole population because it’s small and/or not a random selection. example: Only interviewing three of your friends and saying their opinion represents the opinion of the whole school

School Bus Riders You want to estimate the number of students in a high school who ride the school bus. Which sample is unbiased? a. 4 students in the hallway b. all students in the marching band c. 50 seniors at random d. 100 students at random during lunch What if you wanted to estimate the number of seniors in a high school who ride the school bus. Which sample is unbiased?

Is it unbiased? Valid? Unbiased: The sampling is as close a representation of the whole as possible. The sampling is also as random as possible and not just picking people you know will agree with you. Valid: Having an unbiased sampling AND the data (math) supporting the conclusion. example: Having results that show 2/6 people want to paint their bedrooms a new color but then you exaggerating this and saying that half of people want to paint their bedroom a new color.

Valid Conclusions You want to know how the residents of your town feel about adding a new stop sign. Determine whether each conclusion is valid. a. You survey the 20 residents who live closest to the new sign. 15 support the sign and 5 do not. So, you conclude that 75% of the residents of your town support the new sign. The sample does not represent the whole population and people who live close to the sign are biased. So the sample is biased and the conclusion is not valid.

Making Predictions IF your samples are random and unbiased, you can use the information you gather (data) to make predictions about a whole population. Example: You write for the newspaper of your new high school and you’ve been tasked with finding out the percentage of students who eat breakfast in the morning. Of the 1200 students in your school, you survey 75 of them randomly. Of the 75 students you spoke to, 50 said that they do eat breakfast in the morning. Use this information to predict the number of students in the whole high school who eat breakfast in the morning.

Homework Pg. 444 (Handout) (#1, 2, 3, 4, 5, 7, 8, 10, 13, 14, 15)