Lesson 7.5 M2 Select & Draw Conclusions from Samples

• A survey is a study of one or more characteristics of a group.

• The entire group you want information about is called a population.

• A sample is a part of the population.

Types of Samples• In a random sample, every member of the

population has an equal chance of being selected.

• In a stratified random sample, the population is divided into distinct groups. Members are selected at random from each group.

• In a systematic sample, a rule is used to select members of the population.

• In a convenience sample, only members of the population who are easily accessible are selected.

Types of Samples• In a self-selected sample, members of the

population select themselves by volunteering.

• A representative sample is a sample that accurately reflects the characteristics of a population.

• A biased sample is a sample that is not representative of the population.

• (A question that encourages a particular response is a biased question.)

Example• A high school is conducting a

survey to determine the average number of hours that their students spend doing homework each week. At the school, only the members of the sophomore class are chosen to complete the survey. Identify the population and classify the method.

Example• A high school is conducting a

survey to determine the average number of hours that their students spend doing homework each week. The school asks students to volunteer to take the survey. Identify the population and classify the method.

Example• The manager of a movie rental

store wants to evaluate how customers rate the selection of movies that the store has in stock. Customers are given comment cards with their receipts. Identify the population and classify the method.

Example• At a family reunion, the next year’s

reunion location is randomly chosen to be at one of the family member’s homes. Each home is put on a slip of paper into a hat. The location is chosen by pulling a name from a hat. Identify the population and classify the method.

Identify biased questions:• Do you still support the school

basketball team, even though the team is having its worst season in 5 years?

• Rephrase:

Identify biased questions:• Don’t you think that dogs are

better pets than cats?• Rephrase:

Margin of Error• The MOE gives a

limit on how much the responses of a sample would differ from the responses of a population.

• When a random sample of size n is taken from a large population, the MOE is approximately…

1n

What does that mean?• This means that if

the percent of the sample responding a certain way is p (represented as a decimal) then the percent of the population that would respond the same way is likely to be between…

1pn

Example• In a survey of 990

workers, 30% said they eat at home during a typical week.

• What is the MOE?

1 0.032 3.2%990

Continued• Now give an interval that is likely to contain

the exact percent of all workers who eat at home during a typical work week.

• 30% -3.2% = 26.8%• 30% + 3.2% = 33.2%• It is likely that the exact percent of all

workers who eat at home during a typical work week is between 26.8% and 33.2%.

Homeworkp. 271 #1-19 odds, 20-23 all