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Unit III Review

Chapters 11-13: Collecting Data

Statistics are used to describe and parameters describe .

Variability (a.k.a. Sampling Error) v. Bias

Which one naturally occurs and is ok?

Which one can be (and should be) avoided?

If bias is present, the results/conclusions are

Every sample has

Which one is the result of poor sampling methods?

Methods of Data Collection:

What kind of conclusion can you draw from each method of data collection?

Random sampling

Experiment

Observational Study

If our results are statistically significant, that means

What’s the difference between retrospective and prospective studies?

The 3 requirements of an experimental design are:

1. 2. 3.

In an experiment,

Randomization reduces

Blocking reduces

Placebos are a form of

The explanantory variable is called

Randomization refers to: I. randomly assigning subjects to treatments

II. randomly selecting subjects

III. both I and II

Exercises:

1. John needs to randomly select 3 of his 10 employees for a job satisfaction survey. Show how this can be done using the information below.

Employees: Avery Charlton Ellis Gabor Ingram

Barker Davis Franklin Holland Jackson

Random Number Table:

8 1 1 8 3 4 8 5 5 4 6 0 8 0 8 3 9 9 9 6 5 0 6 9 2 1 8 9 7 7 2 8 3 7 0

2. Sam is preparing sweet potato pies as his dessert for Thanksgiving. The store he shops at sells six sweet potatoes in a bag. He has found that each bag will contain either 0, 1 or 2 bad sweet potatoes. Based on experience he estimates that there will be no bad sweet potatoes in 40% of the bags, one bad sweet potato in 30% of the bags, and two bad sweet potatoes in the rest. Conduct a simulation to estimate how many bags Sam will have to purchase to have 3 dozen good sweet potatoes.

a. Describe how you will use a random number table to conduct the simulation.

b. Show three trials by clearly labeling the random number table given below.

Specify the outcome of each trial.

Trial 1: 1 0 2 4 2 5 0 6 9 2 1 8 9 7 7 2 8 3 7 0 8 2 6 6 9 8 3 2 3 6 7 7 4 7 9

Trial 2: 9 0 6 1 8 4 3 7 0 7 7 8 6 9 5 8 1 1 8 3 4 8 5 5 4 6 0 8 0 8 3 9 9 9 6

Trial 3: 8 1 9 1 5 2 8 4 0 4 3 3 3 6 6 9 2 0 8 2 0 4 8 2 2 7 9 8 6 6 0 6 7 6 5

3. Which type of bias is present in each situation?

a. randomly selecting 100 names from a phone book

b. TV news surveys where viewers are asked to call in

c. a survey question states “Are you in favor of using abortion to kill unwanted babies?”

d. a survey is given to 20 of your classmates, but only 15 return it to you

e. a survey about job satisfaction for school employees is given by selecting one department

(teachers, administrators, custodians, etc) at random

4. A member of the City Council has proposed a resolution opposing construction of a new state prison there. The council members decide they want to assess public opinion before they vote on this resolution. Below are some of the methods that are proposed to sample local residents to determine the level of public support for the resolution. Match each with one of the listed sampling techniques.

a. Place an announcement in the newspaper asking people to call their council reps to register their opinions. Council members will tally the calls they receive.

b. Have each council member survey 50 friends, neighbors, and co-workers.

c. Have the Board of Elections assign each voter a number, then select 400 of them using a random number generator.

d. Go to a downtown street corner, a grocery store, and a shopping mall; interview 100 typical shoppers at each location

e. Randomly pick 50 voters from each election district

f. Call every 500th person in the phone book

g. Randomly pick several city blocks, then randomly pick 10 residents in each block

h. Randomly select several city blocks; interview all adults living in each block

5. A basketball player has a 70% free throw percentage. Estimate the number of free throws she will make on her next 5 attempts.

Trial 1: 1 8 9 7 7 2 8 3 7 0 8 2 6 6 9 8 3 2 3 6 7 7 4 7

Trial 2: 7 8 6 9 5 8 1 1 8 3 4 8 5 5 4 6 0 8 0 8 3 9 9 9 6

Trial 3: 3 3 3 6 6 9 2 0 8 2 0 4 8 2 2 7 9 8 6 6 0 6 7 6 5

6. Which method would be the best for gathering the following data? (census, sample, observation, experiment)

a. you want to find out how US adults feel about cloning

b. you want to determine if Tide or All works better on grass stains

c. you want to find out if students who take AP classes are more likely to finish college

d. you want to determine the average GPA of students taking AP Stats at your school

7. A researcher wants to compare the effect of a new type of shampoo on hair condition. The researcher believes that men and women may react to the shampoo differently. Additionally, the researcher believes that the shampoo will react differently on hair that is dyed. The subjects are divided into four groups: men who dye their hair (4 subjects), men that don’t dye their hair (28 subjects), women who dye their hair (18 subjects) and women who don’t dye their hair (16 subjects). Subjects in each group are randomly assigned to the new shampoo or old shampoo, without knowing which they are given.

a. Identify the subjects.

b. How many factors are there and how many levels of each?

c. Is the experiment blocked? If so, how?

d. How many treatments are there?

e. Is the experiment blinded? Explain.

f. What is the response variable.

g. Draw a diagram representing the experimental design.

8. A researcher was interested in determining the effects of class size (small, med, lg) and the use of a traditional textbook versus a new textbook. The researcher conducted her own experiment, assigning each combination of class size and type of book to 12 randomly selected classes at schools in the district. The average final grade of each class was recorded at the end of the year.

a. What are the factors/levels?

b. How many treatments are there?

c. What are the experimental units? How many are there?

d. What is the response variable?

Sketch a diagram.

9. Researchers who wanted to see if drinking grape juice could help people lower their blood pressure got 120 non-smokers to volunteer for a study. They measured each person’s blood pressure and then randomly divided the subjects into two groups. One group drank a glass of grape juice every day while the other did not. After sixty days the researchers measured everyone’s blood pressure again. They reported that differences in changes in blood pressure between the groups were not statistically significant.

a. Was this an observational or experimental study? Explain.

b. Briefly explain what “not statistically significant” means in the context of this study.

c. Was this experiment completely randomized or blocked?

d. Since everyone’s blood pressure was measured at the beginning and end, the researchers could have simply looked at the grape juice drinkers to see if their blood pressure changed. What is the other group called and why would they be included in the experiment?

e. They plan to repeat the experiment with both non-smokers and smokers to determine if smoking is a factor. How should their design strategy differ?

Multiple Choice practice

# 1 – 2 An insurance company conducted a study to determine the percent of cardiologists who had been sued for malpractice during the past five years.

1. The population of interest is:

a. the set of all doctors who were sued for malpractice

b. the set of cardiologists who were sued for malpractice

c. all doctors

d. all cardiologists

e. all doctors who have malpractice insurance

2. Which of the following could be used to gather the data?

a. a designed experiment

b. a census of all cardiologists

c. an observational study of randomly selected cardiologists

d. a survey sent tot randomly selected cardiologists

e. any answer except (a.)

3. An auto analyst is conducting a satisfaction survey, sampling from a list of 10,000 new car buyers. The list includes 2500 Ford buyers, 2500 GM buyers, 2500 Honda buyers, and 2500 Toyota buyers. The analyst selects a sample of 400 car buyers, by randomly sampling 100 buyers of each brand. Is this an example of a simple random sample?

a. yes, because each buyer in the sample was randomly sampled

b. yes, because each buyer in the sample had an equal chance of being sampled

c. yes, because car buyers of every brand were equally represented in the sample

d. no, because every possible 400-buyer sample did not have an equal chance of being chosen

e. no, because the poplation consisted of purchasers of four different brands of car

4. The main way to protect against confounding is to

a. use an observational study d. repeat the treatment on many units

b. assign treatments randomly to subjects e. none of the above

c. use a placebo

5. Blocking will be effective only if

a. all units in one block receive the same treatment

b. each subject receives all treatments

c. units are grouped so that each block contains units that are different

d. units are grouped so that each block contains units that are similar

e. units are grouped so that each block is representative of the population

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