Statistics Exam 1

Ch 1 and 2

Statistic

A numerical summary of a sample

Descriptive Statistics

Organizing and summarizing data through tables, graphs, and numerical summaries

Statistics

The science of collecting, organizing, summarizing, and analyzing information to draw conclusions or answer questions. It is also about providing a measure of confidence in any conclusion

Sample

A subset of the group of individuals that is being studied

Inferential Statistics

Uses methods that take results from a sample and extends them to the population, and measures the reliability of the result

Individual

A person or object that is a member of the group being studied

Parameter

A numerical summary of a population

Population

The entire group of individuals to be studied

Descriptive Statistics

consists of organizing and summarizing information

Inferential Statistics

uses methods that generalize results obtained from a sample to the population and measure the reliability of the results

The variable is quantitative because it is a numerical measure

Determine whether the variable is qualitative or quantitative. Amount of money won in a lottery

The variable is continuous because it is not countable

Determine whether the quantitative variable is discrete or continuous. Length of rock song

The variable is discrete because it is countable

Determine whether the quantitative variable is discrete or continuous. Number of field goals attempted by a kicker

Adult women who are 30 to 70 years of age and live in the United States.

A polling organization contacts 2940 adult women who are 30 to 70 years of age and live in the United States and asks whether or not they had received a mammogram during the past year.

What is the population in the study?

The 2940 adult women who are 30 to 70 years of age and live in the United States.

A polling organization contacts 2940 adult women who are 30 to 70 years of age and live in the United States and asks whether or not they had received a mammogram during the past year.

What is the sample in the study?

Confounding

**Occurs when the effects of two or more explanatory variables are not separated. Therefore, any relation that may exist between an explanatory variable and the response variable may be due to some other variable not accounted for in the study**

Confounding Variable

**An explanatory variable that was considered in a study whose effect cannot be distinguished from a second explanatory variable in the study**

Designed Experiment

**A researcher randomly assigns the individuals in a study to groups, intentionally manipulated the value of an explanatory variable, controls other explanatory variables at fixed values, and then records the value of the response variable for each individual**

Lurking Variable

**An explanatory variable that was not considered in a study, but that affects the value of the response variable in the study. In addition, this variable is typically related to other explanatory variables in the study**

Observational Study

**A researcher measures the value of the response variable without attempting to influence the value of either the response or explanatory variables. That is, the researcher observes the behavior of individuals in the study and records the values of the explanatory and response variables**

Cohort Study

**Studies that follow a group of individuals over a long period of time. Characteristics of the individuals are recorded and some individuals will be exposed to certain factors (not intentionally) and others will not. Because the data are collected over time, these studies are prospective**

Case-Control Study

**Studies that are retrospecitve, meaning they require the researcher to look at existing records, or the subject to recall information from the past. Individuals who have certain characteristics are matched with those who don't**

Cross-sectional study

**Studies that collect information about individuals at a specific point in time, or over a short period of time**

A retrospective study requires that individuals look back in time or require the researcher to look at existing records

What does it mean when an observational study is retrospective?

A prospective study collects the data over time.

What does it mean when an observational study is prospective?

A frame is a list of the individuals in the population being studied.

What is a frame?

simple random sampling

A sample of size n from a population of size N is obtained through simple random sampling if every possible sample of size n has an equally likely chance of occurring. The sample is then called a simple random sample.

Once an individual is selected, the individual cannot be selected again.

What does it mean when sampling is done without replacement?

Systematic

Which sampling method does not require a frame?

Cluster sample

is obtained by dividing the population into groups and selecting all individuals from within a random sample of the groups

stratified sample

is obtained by dividing the population into homogeneous groups and randomly selecting individuals from each group

sampling bias

The techniques used to select individuals to be in the sample favor one part of the population over another

Response bias

The answers on a survey do not reflect the true feelings of the respondent

Bias

The results of the sample are not representative of the population.

Nonresponse Bias

The individuals selected to be in the sample who do not respond to the survey have different opinions from those who do respond

Response Variable

A quantitative or qualitative variable that represents the variable of interest

Factor

The variable whose effect on the response variable is to be assessed by the experimenter

Experimental Unit

A person, object, or some other well-defined item upon which a treatment is applied

Treatment

Any combination of the values of the factors (explanatory variables)

Placebo

A treatment that looks just like the "real" treatments in a study. Could be an innocuous medication or a procedure that follows the same steps as the experimental procedure, but leaves out a key intervention

Confounding

The effect of two factors (explanatory variables) on the response variable cannot be distinguished

Blinding

Nondisclosure of the treatment an experimental unit is receiving

Replication is applying each treatment to more than one experimental unit.

What is replication in an experiment?

Difference between a single-blind and double-blind experiment

In a single-blind experiment, the subject does not know which treatment is received. In a double-blind experiment, neither the subject nor the researcher in contact with the subject knows which treatment is received.

Blocking

Grouping together similar experimental units and then randomly assigning the experimental units within each group to a treatment

Number; proportion

A frequency distribution lists the ___ of occurrences of each category of data, while a relative frequency distribution lists the ____ of occurrences of each category of data

1

In a relative frequency distribution, what should the relative frequencies add up to?

Bar graph

a horizontal or vertical representation of the frequency or relative frequency of the categories. The height of each rectangle represents the category's frequency or relative frequency.

Pareto chart

bar graph whose bars are drawn in decreasing order of frequency or relative frequency.

Classes

the categories by which data are grouped

Lower, upper

The __ class limit is the smallest value within the class and the ________ class limit is the largest value within the class

Class Width

the difference between consecutive lower class limits

Skewed-right

For jewelry prices in a jewelry store, state whether you would expect a histogram of the data to be bell-shaped, uniform, skewed left, or skewed right

All the observations are less than or equal to the last class

the cumulative relative frequency for the last class must always be 1. Why?