Chapter 1: Introduction to StatisticsTest Review

1-1 Overview• Data• Statistics• Population• Census• Sample

1-1 Overview• Sample data must be collected in an appropriate way, such as

through a process of selection.

• If sample data are not collected in an appropriate way, the data may be

.

1-2 Types of Data• parameter• statistic• Quantitative data• Qualitative data• Discrete data• Continuous data

• Levels of Measurement• Nominal• Ordinal• Interval• Ratio

1-3 Critical Thinking

• Voluntary response sample

• Statistical Misrepresentations• Small samples• Graphs• Pictographs• Percentages• Loaded questions• Order of questions• Nonresponse

• Missing data• Correlation and causality• Self-interest study• Precise numbers• Partial pictures• Deliberate distortions

1-4 Design of Experiment• Observational study• Experiment• Experiment units• Cross-sectional study• Retrospective study• Prospective study• Confounding

• Random sample• Simple random

sample• Probability sample• Systematic sampling• Convenience sampling• Stratified sampling• Cluster sampling• Sampling error• Nonsampling error

Review Questions

1. Sampling Shortly after the World Trade Center towers were destroyed by terrorists, America Online ran a poll of its Internet subscribers and asked this question: “Should the World Trade Center towers be rebuilt?” Among the 1,304,240 responses, 768,731 answered “yes,” 286,756 answered “no,” and 248,753 said that it was “too soon to decide.” Given that this sample is extremely large, can the responses be considered to be representative of the population of the United States? Explain.

Review Questions

2. Sampling Design You have been hired by Verizon to conduct a survey of cell phone usage among the full-time students who attend your college. Describe a procedure for obtaining a sample of each type:

a. Randomb. Systematicc. Convenienced. Stratifiede. Cluster

Review Question

3. Identify the level of measurement (nominal, ordinal, interval, ratio) used in each of the following:

a. The weights of people being hurled through the air at an enthusiastic rock concert.

b. A movie critic’s ratings of “must see, recommended, not recommended, don’t even thing about going”

c. A movie critic’s classification of “drama, comedy, adventure”d. Bob, who is different in many ways, measures time in days,

with 0 corresponding to his birth date. The day before his birth is -1, the day after his birth is +1, and so on. Bob has converted the dates of major historical events to his numbering system.

Review Question4. Coke The Coca Cola Company has 366,000 stockholders and a

poll is conducted by randomly selecting 30 stockholders from each of the 50 states. The number of shares held by each sampled stockholder is recorded.

a. Are the values obtained discrete or continuous?b. Identify the level of measurement for the sample data.c. Which type of sampling is being used?d. If the average (mean) number of shares is calculated, is the

result a statistic or a parameter?e. If you are the CEO of the Coca Cola Company, what characteristic

of the data would you consider to be extremely important?f. What is wrong with gauging stockholder views by mailing a

questionnaire that the stockholders could complete and mail back?

Review Question

5. More Coke Identify the type of sampling used when a sample of 366,000 Coca Cola shareholders is obtained as described. Then determine whether the sample scheme is likely to result in a sample that is representative of the population of all 366,000 shareholders.

a. A complete list of all stockholders is compiled and every 500th name is selected.

b. At the annual stockholders’ meeting, a survey is conducted of all who attend.

c. Fifty different stockbrokers are randomly selected, and a survey is made of all their clients who own shares of Coca Cola.

d. All the stockholders zip codes are collected, and 5 stockholders are randomly selected from each zip code.

Review Question

6. Design of Experiment You plan to conduct an experiment to test the effectiveness of Sleepeze, a new drug that is supposed to reduce insomnia. You will use a sample of subjects that are treated with the drug and another sample of subjects that are given a placebo.

a. What is “blinding” and how might it be used in this experiment?

b. Why is it important to use blinding in this experiment?c. What is a completely randomized design?d. What is a rigorously controlled design?e. What is replication, and why is it important?

Review Question

7. Honest Abea. When Abraham Lincoln was first elected to the presidency, he

received 39.82% of the 1,865,908 votes cast. The collection of all those votes is the population being considered. Is the 39.82% a parameter or a statistic?

b. Part (a) gives the total votes cast in the 1860 presidential election. Consider the total numbers of votes cast in all presidential elections. Are those values discrete or continuous?