Chapter 1



Quiz 1.1A Name:

1. A psychologist wants to know if college students with normal vision and adults with normal vision can be fooled by a certain optical illusion. She recruits 50 students from across her university and 50 adults from the town, shows them the optical illusion and finds that 42 of the students and 39 of the adults are fooled by the illusion. The population in this study is

(a) the 42 students who were fooled.

(b) the 50 students who served as subjects.

(c) all students in the PSY 120 class.

(d) all adults with normal vision.

2. The psychologist in the previous question carried out:

(a) a census

(b) an experiment

(c) an observational study

(d) a sample survey

3. You are thinking about purchasing a cell phone. Before making a decision, you contact the major service providers in your area to obtain some information. For each service provider, you record the cost of the phone itself, the required length of the service contract, whether the phone gives you access to the internet, and the average cost per minute for 500 minutes of monthly use.

(a) What are the individuals in this data set?

(b) What variables are you recording for each individual? Circle the numerical variables.

4. Over the last few weeks, you have been finding that your statistics homework takes you an extremely long time each night. Your teacher suggests that you determine how long other members of the class are spending on the homework assignments, so that you will know where you stand in comparison. Would it be best to gather the data on homework time by a sample survey or a census? Justify your answer.

5. Do Major League Baseball games take less time now than they did last season? To try to answer this question, you obtain data on the lengths of all games played in each of the two seasons. Since there were thousands of games played each season, you decide to select the first 100 games played in each of the two seasons. Then, you compute the average game length for this season and for last season.

(a) Is this an experiment or an observational study? Explain.

(b) Describe the population(s) of interest and the sample(s) chosen in this situation.

(c) Do you think the sample(s) chosen will provide accurate information about the lengths of baseball games? Why or why not?

6. In October 2007, 543 randomly selected subscribers of the Money Management magazine of a national consumer organization were asked how many store membership or discount/buying bonus cards they carried with them. The bar chart below summarizes the data.

[pic]

a) Is this an observational study or an experiment? Justify your answer.

b) Approximately what percent of the surveyed subscribers carry 5 or less cards with them?

c) Do you think that this survey will tell you about the number of store or discount/bonus buying cards carried by U.S. consumers in general? Explain your answer.

Quiz 1.2A Name:

1. Below are the dotplots of the stadium capacity of all major league baseball teams in 2008 organized by National and American Leagues.

[pic]

a) Is this a sample or a census? Explain your answer.

b) In a few sentences compare the seating capacity of American League versus National League baseball stadiums.

2. In a recent survey of members of the American Association of Retired Persons, about 9% stated they had attained less than a high school diploma. The pie chart below also indicates that 26% were high school graduates, 32% had some college, and 33% possessed at least a 4-year degree.

[pic]

a) What was a reasonable question of interest in this case?

b) Do you think these results were obtained using an observational study or an experiment? Explain.

c) Who are the individuals in this study? What variable was measured? Is the variable categorical or quantitative?

d) What percent of the sample have at least some college in their background?

3. Berkeley saw a commercial where the company claimed that it made the strongest paper towel. She decided to test their claim against three other brands of paper towels. Berkeley soaked a sheet of paper towel for three seconds and then suspended the sheet across a baking pan using small clamps to hold the sheet in place. Carefully she began to place pennies on the paper towel sheet until it ripped. Berkeley repeated this four times for each brand of paper towel, each time counting the number of pennies that the towel held before breaking.

The data she recorded is below.

|Towel A |43 |51 |59 |39 |

|Towel B |105 |89 |111 |91 |

|Towel C |53 |45 |61 |41 |

|Towel D |87 |79 |92 |85 |

a) Is this an observational study or an experiment? Explain.

b) Identify two sources of variation that might exist in this study. Explain how this variation might affect the results.

c) What might Berkeley conclude from her study?

4. When the discussion turns to the pros and cons of wearing automobile seat belts, Herman always brings up the case of a friend who survived an accident because he was not wearing a seat belt. The friend was thrown out of the car and landed on a grassy bank, suffering only minor injuries, while the car burst into flames and was destroyed. Explain to Herman why this does not provide good evidence that it is safer not to wear seat belts.

Chapter 1: Quiz and Test Solutions

Quiz 1.1A

1. (choice d) While the two samples was drawn from across the university and the town there appears to be little reason to believe that normal vision in the two groups is somehow different from normal vision in the general population.

2. (choice d) The psychologist did not impose a treatment so it is not an experiment. She just showed the students and the townspeople a card and asking them what they saw.

3. (a) The cell phone service providers. (b) Phone cost, length of service contract, access to the Internet, average cost per minute for 500 minutes of monthly use; all but the variable access to the Internet are numerical.

4. A census of the entire class seems the most practical and instructive way to collect relevant data. You can’t really do an experiment or an observational study in this case, and you may as well include the entire population of the class in the survey.

5. (a) This is a comparative observational study with the information provided. No treatment was imposed that we are aware of. This is not a survey of any kind. We are merely looking at data. (b) Populations: all Major League Baseball games played last season, all Major League Baseball games played this season; Samples: first 100 games played last season, first 100 games played this season. (c) Perhaps not. There may be some characteristic of the first 100 games of a season that tends to make them longer or shorter than games throughout the rest of the season.

6. (a) This is an observational study. (b) A rough estimate is 48% + 42% = 90%

(c) No. Only subscribers to the Money Management magazine were surveyed and this group by virtue of their subscription may be different that the general population of U.S. consumers.

Quiz 1.2A

1. (a) This is a census since all MLB ballparks are included from 2008. (b) There appears to be somewhat more variability in the seating capacity of American League ballparks. While the overall range is about the same, the National League ballparks seem to be more concentrated around capacities of 42,000, whereas the seating capacity of American League stadiums is more uniformly spread out. The National League claims the largest stadium at nearly 56,000 seats, whereas the two smallest stadiums are in the American League. A typical National league stadium seats 42,000 while the typical American League stadium seems to seat about 43,500.

2. (a) “What is the education level of AARP members?” (b) This is an observational study and there was no active intervention of the subjects. (c) Population: members of the American Association of Retired Persons; Variable: educational level attained; it is a categorical variable. (d) 65%

3. (a) Berkeley has conducted an observational study.. She selected 4 brands of towels, wet them, and then counted the number of pennies needed to tear the towel. (b) Answers will vary. If she was not consistently careful when placing the pennies, the force of placing the penny on the towel might tear the towel prematurely. If she mistakenly soaked one of the towels for a longer length of time, it could weaken the towel and it might not hold as many pennies. If she clamped the towels differently it might affect the integrity of the towel and the tearing was due more to the clamping mistake and not to the pennies added. There could also be variation between the brands of towels and between individual towels in the same roll.

(c) Based on the data presented in the problem, it looks like Towel B appears to be stronger than its competitors with Towel D coming in second.

4. Herman is relying on personal experience. He should look at the results from a large number of automobile accidents in which seatbelts were and were not used and compare the injury rates between the two groups.

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