Lesson 8.2.1

HW: 8-35 to 8-40

Learning Target: Scholars will analyze methods of sampling and critique how well a sample represents a certain population. If you want to know what a bowl of soup tastes like, do you need to eat all of the soup in the bowl? Or can you get a good idea of the taste by trying a small sample? When you conduct a survey, it is not usually possible for you to survey every person in the population you are interested in, such as all female teenage shoppers or all of the students at your school. Instead, statisticians collect information about a sample (a portion) of the population. However, finding arepresentative sample (a sample that represents the whole population well) is not easy.

8-29. As the social director of the Class Council, Ramon would like to survey a few students about their interests.

When Ramon analyzes the results from the survey, he wants to make claims about the interests of all of the students in his school. If he were to survey only students on the Class Council, for example, it might be hard to make claims about what all students think. Students who are on the Class Council may not have the same social interests as other students. Consider this idea as you think about the samples described below.

  1. If Ramon wanted to generalize the opinions of all students at his school, would it make sense to go to the grocery store and survey the people there? Why or whynot?
  2. If he wanted to generalize the opinions of all students at his school, would it make sense to ask all of his friends at school? Why or why not?
  3. If he wanted to generalize the opinions of all students at his school, would it make sense to ask every third person who entered the cafeteria at lunch? Why or why not?

8-30. There are a variety of ways to choose samples of the population you are studying. Every sample has features that make it more or less representative of the larger population. For example, if you want to represent all of the students at your school, but you survey all of the students at school 30 minutes after the last class has ended, you are likely to get a disproportionate number of students who play school sports, attend after-school activities, or go to after-school tutoring.

  1. If you ask the opinion of the people around you, then you have used a convenience sample. If you took a convenience sample right now, what would be some features of the sample? Would you expect a convenience sample to represent the entire student population at your school? Why or why not?
  2. If you email or create an online questionnaire then you have used a voluntary response sample. What are some features of the people in a volunteer response sample? Could it represent the sample of all of the students at school accurately?
  3. You use a cluster sample if you first divide the students into smaller groups so that each of the smaller groups represents all of the students at your school. Then you randomly select one or more of these groups to sample. How might you divide the students at your school into groups that each represent the whole school? Explain. Are there any reasons that these clusters might not be fully representative of all the students at your school?

8-31. From what population is each of these samples taken? Write down the actual population for each of these sampling techniques.

8-32. A study at the University of Iowa in 2008 concluded that children that play violent video games are more aggressive in real life. Children ages 9 to 12 were studied to determine how much they played violent video games; peers and teachers were asked how much these students hit, kicked, and got into fights with other students.

  1. Can you legitimately conclude from this study that teenagers who play violent video games tend to be more aggressive? Why or why not?
  2. Can you legitimately conclude from this study that children ages 9 to 12 who play violent video games are more likely to commit violent crimes? Why or why not?
  3. Can you legitimately conclude from this study that children ages 9 to 12 who play violent video games tend to hit and kick more in school?
  4. Can you legitimately conclude from this study that playing a lot of violent video games will cause 9 to 12-year-old students to become more violent at school?

8-33. Addie was helping children in a kindergarten class learn to read. She was curious how old the typical child was when they entered kindergarten. It was not practical to look up the school records of all 100 kindergarteners. So on the first day of school, Addie took a sample: she asked the parent of the first fifteen students to be dropped off at the school how old (in months) their child was. Her data is listed below.

 67 61 69 72 71 65 67 67 57 68 71 72 61 59 62

Makean inference (a statistical prediction) of the mean age of Kindergarten children at theschool.

8-35.Suppose you were conducting a survey to try to determine what portion of voters in your small town support a particular candidate for mayor. Consider each of the following methods for sampling the voting population of your town. State whether each is likely to produce a representative sample and explain your reasoning.

  1. Ask every voter on your block.
  2. Randomly pick one house from each block in the neighborhood and survey the homeowner.
  3. Survey each person at the I-Jump Pancake Restaurant after church on Sunday morning.
  4. Ask people who are leaving the twice-yearly town hall meeting.
  5. Visit every tenth person on the county’s voter registration list.

8-36.Calculate the percent change in each problem below.

  1. Robert wanted to buy a computer game that cost $25 last week. This week when he went back to buy the game, the price was $35. What was the percent of increase in the price?
  2. Susan bought a jacket on sale. The original price of $35 was marked down to $25. What was the percent discount because of the sale?
  3. Why were your answers to parts (a) and (b) different?

8-37. Simplify each expression.

8-38. Findthe area and perimeter of each shape below. Show your steps and work. Note: Diagrams are not drawn to scale.

8-39.Therecommended speed on a scenic road is 35 mph. Driving too fast is a hazard, but so is driving too slowly. Safe speeds s may be described by the inequality.

  1. Find a list of at least 5 safe speeds.
  2. Determinehow to show the entire set of possible values (solutions) for s by graphing them on a number line.

8-40.Simplify and solve each equation below forx. Show your work and check your answer.

  1. 24 = 3x + 3
  2. 2(x − 6) = x − 14
  3. 3(2x − 3) = 4x − 5
  4. = 2x– 5

Lesson 8.2.1

  • 8-29.See below:
  • No. That sample probably does not go to your school.
  • No. The students who are not his friends might have different sorts of opinions than his friends.
  • No. While this is the best sample yet, it still does not include students who bring their own lunch or who do not otherwise eat in the cafeteria.
  • 8-30.See below:
  • Students taking this math class. No. Reasons vary.
  • They are people who regularly use a computer and who choose to respond. Probably not; students may argue that people most likely to respond are people who feel most strongly about the issues being surveyed.
  • Some clusters might be: students in a homeroom depending on how homerooms are selected; students in areas of the school at break (near the square, near the cafeteria); students sitting in sections at a school-wide assembly; students attending on a certain registration day.
  • 8-31.See answers in bold in table below.
  • 8-32.See below:
  • No. The sample did not include teenagers.
  • No. Crimes rates were not studied.
  • This study does indicate a relationship.
  • No, it can only be said that there is a relationship between the two; which is the cause and which is the effect is not known; it might be that violent students are more attracted to violent video games.
  • 8-33.65.9 months
  • 8-35.See below:
  • Not representative; neighborhoods in towns tend to have different characteristics from each other like wealth, ethnic makeup, proximity to services, traffic, etc.
  • Fairly representative; but this will also survey non-voters; it would be better to survey only voters.
  • Not representative; this samples the population of people who attend church and who favor the particular pancake restaurant and have the time and money for a leisurely brunch.
  • Possibly; it might be pretty representative because you will get active citizens who are also more likely to vote; but if a “hot topic” is on the agenda, you might get mostly those who are passionate about the one agenda item.
  • This sample is just about the best you are going to get for a representative sample of voters.
  • 8-36.See below:
  • The price increased by 40%.
  • 28.6%
  • Sample response: Each percentage was related to a different whole or original price.
  • 8-37.See below:
  • or
  • −or −6
  • or 3
  • 8-38.See below:
  • A= 420 sq. units,P= 112 units
  • A= 744 sq. units,P=186 units
  • 8-39. See below:
  • Solutions will be between 25 and 45mph
  • See solution below.
  • 8-40.See below:
  • x = 7
  • x =−2
  • x = 2
  • x = 4