Name ______Date ______

Math 7ACBiased and Unbiased Samples

Do Now: A TV programming manager wants to conduct a survey to determine which reality television show is the favorite of viewers in a certain viewing area. He is considering the three samples shown below. Draw an X through the two samples that would not fairly represent all of the people in the viewing area.

Explain why the two samples that you crossed out do not fairly represent all of the people in the viewing area.

Data gathered from a representative sample can be used to make predictions about a population.

*An unbiased sample is selected so that it is representative of the entire population.

Types of Unbiased Samples:

Type / Description / Example
Simple Random Sample
Systematic Random Sample

*In a biased sample, one or more parts of the population are favored over others.

Types of Biased Samples:

Type / Description / Example
Convenience Sample
Voluntary Response Sample

EXAMPLES: Determine what type of sample each example is and whether each sample is valid. Justify your answer.

1)To determine the favorite dog breed of people who enter dog shows, every fifth person entering a dog show is surveyed.

2)To determine what type of pet people prefer, the spectators at a dog show are surveyed.

3)DENTISTRYA survey is to be conducted to determine the reasons dental patients are hesitant to go to the dentist. Describe the sample and explain why each sampling method might not be valid.

a)Adults that are randomly selected from an office complex are asked to go online and fill out a questionnaire.

b)A randomly selected dentist asks his patients why they may be hesitant to go to a dentist.

c)Randomly selected dental patients who are having a routine check-up are asked to write down their feelings.

______

5) A random survey of the students in eighth grade shows that 7 prefer hamburgers, 5 prefer chicken, and 3 prefer hot dogs.

a) Is the sample valid? What percent prefer hot dogs?

b)If 120 students will attend the eighth grade picnic, how many hot dogs should be ordered for each student to get one?

______

6)To determine the most common injury cared for in an emergency room, a reporter goes to the same hospital every afternoon for one month during the summer and observes people entering the emergency room. She concludes that second degree sunburn is the most common injury.

7)To evaluate customer satisfaction, a grocery store gives double coupons to anyone who completes a survey as they enter the store. The store manager determines that customers are very satisfied with their shopping experience in his store.

Name ______Date ______

Math 7ACBiased and Unbiased Samples HW

Determine whether each conclusion is valid and state the type of sample used. Justify your answer.

1)To award prizes at a hockey game, four tickets with individual seat numbers printed on them are picked from a barrel. Since Elvio’s section was not selected for any of the four prizes, he assumes that they forgot to include the entire section in the drawing.
2)To award prizes at a hockey game, four tickets with individual seat numbers printed on them are picked from a barrel. Since Elvio’s section was not selected for any of the four prizes, he assumes that they forgot to include the entire section in the drawing.
3)To evaluate the quality of the televisions coming off the assembly line, the manufacturer takes one every half hour and tests it. About 1 out of every 10,000 is found to have a minor mechanical problem. The company assumes from this data that about 1 out of every 10,000 televisions they produce will be returned for mechanical problems after being purchased.
4)To determine whether most students participate in after-school activities, the principal of Humberson Middle School randomly surveyed 75 students from each grade level. Of these, 34% said they participate in after school activities. The principal concluded that about a third of the students at Humberson Middle School participate in after school activities.
5)A television program asked its viewers to dial one of two phone numbers indicating their preference for one of two brands of shampoo. Of those that responded, 76% said they prefer Brand A. The program concluded that Brand A was the more popular brand of shampoo.
6)To evaluate the defect rate of its memory chips, an integrated circuit manufacturer tests every 100th chip off the production line. Out of 10 chips tested, one chip is found to be defective. The manufacturer concludes that 3 chips out of 3,000 will be defective.
7)To determine if the class understood the homework assignment, the math teacher checks the top 3 papers in the pile of collected homework. The teacher finds that all students understood the homework assignment.

DININGOUTFor Exercises 8 and 9, use the following information. As people leave a restaurant one evening, 20 people are surveyed at random. Eight people say they usually order dessert when they eat out.

8)Is the sample valid? What percent of those surveyed say they usually order dessert when they eat out?
9)If 30 people have dinner at the restaurant tomorrow, how many would you expect to order dessert?