MR. GONZALEZ ALGEBRA 2 Intro to Statistics

Population and Sample What’s the difference?  A population is all the members of a set.  A sample is part of a population Example  Population: Mater Academy  Sample: Class of 2018

Different Sampling Methods Convenience Sample Self-Selected Sample Systematic Sample Random Sample

Convenience Sample For a convenience sample, select any members of the population who are conveniently and readily available Example  Mr. G takes a sample of the students in his class

Self-Selected Sample For a self-selected sample, select only members of the population who volunteer for the sample study. Example  Mr. G invites students to come after school to do a study in his classroom

Systematic Sample For a systematic sample, order the population in some way, and then select from it at regular intervals Example  Mr. G gives all his students a number from 1 to 180, but then he only uses students who’s numbers are multiples of 3

Random Sample In a random sample, all members of the population are equally likely to be chosen Example  Mr. G walks around the halls and picks 50 random students to make a sample

Bias A sample has a bias when a part of a population is overrepresented or underrepresented A bias is a systematic error introduced by the sampling method Example  Mr. G does a survey about exercising after school. More than half of the sample are athletes in the school

Study Methods Observational Study Controlled Study Survey

Observational Study In an observational study, you measure or observe members of a sample in such a way that they are not affected by the study Example  Mr. G, does a study of his class. He observes if there is a connection to the students that did not pass his first test and the students that did not do their homework.

Controlled Experiment In a controlled experiment, you divide the sample into two groups. You impose a treatment on one group but not the other “control” group. Then you compare the effect on the treated and the control group. Example  Mr. G reviews for an test with period 1 and not with period 2. After the test, he compares the results of the two classes.

Survey In a survey, you ask every member of the sample a set of questions. Example  Mr. G asks all his classes a series of questions pertaining to the last test they took in class

Practice Questions What is the sampling method used for each situation? Does the sample have a biased? 1. A newspaper article on the tax increase invites readers to express their opinions on the newspapers' website. 2. A reporter interviews people leaving the city’s largest park 3. A survey service calls every 50 th listing from the local phone book

Practice Question Answers 1. A newspaper article on the tax increase invites readers to express their opinions on the newspapers' website.  Self-selected sample. It might have a bias, depending on who visits the website. 2. A reporter interviews people leaving the city’s largest park  Convenience sample. It might have a bias, depending on what the study was about. 3. A survey service calls every 50 th listing from the local phone book  Systematic Sample. It might have a bias, depending if there is a connection between the people who are listed or not listed

Practice Questions Which type of study method is described in each situation? Should the sample statistics be used to make a general conclusion about the population? 1. Researchers randomly choose two groups from 10 volunteers. Over a period of 10 weeks, one group eats ice cream before going to sleep, and the other does not. Volunteers were monitoring devices while sleeping, and researchers record dream activity. 2. Students in a science class record the height of bean plants as they grow.

Practice Question Answers 1. Researchers randomly choose two groups from 10 volunteers. Over a period of 10 weeks, one group eats ice cream before going to sleep, and the other does not. Volunteers were monitoring devices while sleeping, and researchers record dream activity.  Controlled study. The statistics are based on such a small sample that they are not reliable as a general conclusion. 2. Students in a science class record the height of bean plants as they grow.  Observational study. The statistics may provide a general conclusion but may not be reliable based the type of soil, sunlight, water, and fertilization