math 146 statistics exam 1 questions and answers

Define statistics

Statistics is the science of​ collecting, organizing,​ summarizing, and analyzing information to draw a conclusion and answer questions. In​ addition, statistics is about providing a measure of confidence in any conclusions.

individual

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

Descriptive statistics

consists of organizing and summarizing information​ collected

inferential statistics

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

Statistic

numerical summary of a sample.

Parameter

a numerical summary of a population.

Determine whether the underlined value is a parameter or a statistic.

Telephone interviews of 6067 adults 18 years of age or older found that only 23% could identify the current vice-president.

The value is a statistic because the 6,076 adults in public restrooms are a sample.

Qualitative (categorical)

Classification of individuals based on some attribution or characteristic

Quantitative

provide numerical measures of individuals

Discrete variable

variable that has either a finite number of possible values or a countable number of possible values.

continuous variable

variable that gas an infinite number of possible values. Can be measured to any level of accuracy.

observational study

measures the value of the response variable without attempting to influence the value of either of the response or explanatory variables

designed experiment

A designed experiment is when a researcher assigns individuals to a certain​ group, intentionally changing the value of an explanatory​ variable, and then recording the value of the response variable for each group.

what is meant by confounding

when the effects of two or more explanatory variables are not separated

lurking variable

an explanatory variable that was not considered in a study, but that affects the value of the response variable 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.

cross-sectional study

observational studies that collect information about individuals at a specific point in time, or over a very short period of time.

case-control study

Retrospective. Require individuals to look back in time or require the researcher to look at existing records.

frame

a list of the individuals in the population being studied.

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.

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.

Determine whether the following statement is true or false. Explain.

Inferences based on voluntary response samples are generally not reliable.

True, because it is often the case that the individuals who volunteer do not accurately represent the population.

Determine whether the following statement is true or false. Explain.

When obtaining a stratified​ sample, the number of individuals included within each stratum must be equal.

False. Within stratified​ samples, the number of individuals sampled from each stratum should be proportional to the size of the strata in the population.

To estimate the percentage of defects in a recent manufacturing​ batch, a quality control manager at General Electric selects every

16th refrigerator that comes off the assembly line starting with the fifth until she obtains a sample of 150 refrigerators. What type of sampling is​ used?

systematic

To determine customer opinion of their food quality​, General Foods randomly selects 110 city blocks during a certain week and surveys all homes within the city blocks. What type of sampling is​ used?

Cluster

IBM wants to administer a satisfaction survey to its current customers. Using their customer​database, the company randomly selects 40

customers and asks them about their level of satisfaction with the company. What type of sampling is​ used?

simple random

A magazine asks its readers to call in their opinion regarding the quality of the articles. What type of sampling is​ used?

convenience

Closed question

Has fixed choices for​ answers. Easier to​ analyze, but limit the responses

Open question

A free-response question.Allow respondents to state exactly how they​ feel, but are harder to analyze due to the variety of answers and possible misinterpretation of answers.

What does it mean when a part of the population is​ under-represented?

A part of the population is​ under-represented when it is proportionally smaller in a sample than in its population.

The survey has bias.​ (a) Determine the type of bias.​ (b) Suggest a remedy.

A polling organization conducts a study to estimate the percentage of households that have high-speed Internet access. It mails a questionnaire to 1899 randomly selected households across the country and asks the head of each household if he or she has high-speed Internet access. Of the 1899 households​ selected, 11 responded.

a) Under coverage bias

b) The polling organization should try contacting households that do not respond by phone or​ face-to-face.

What are the advantages of having a presurvey with open questions to assist in constructing a questionnaire that has closed​ questions?

The researcher can learn common answers.

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)

response variable

The quantitative or qualitative variable for which the experimenter wishes to determine how its value is affected by the explanatory variable

factor

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

placebo

An innocuous​ medication, such as a sugar​ tablet, that​ looks, tastes, and smells like the experimental medication

confounding

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

single-blind

An experiment in which either the subjects or those who interact with them and measure the response variable, but not both, know which treatment a subject received.

double-blinded

neither the subject nor the researcher in contact with the subject knows which treatment is received.

To help assess student learning in her developmental physics ​courses, a physics professor at a university implemented​ pre- and​ post-tests for her developmental physics students. A​ knowledge-gained score was obtained by taking the difference of the two test scores.

What type of experimental design is​ this?

matched pair

frequency distribution

lists the number of occurrences of each category of​ data, while a relative frequency distribution lists the

the proportion of occurrences of each category of data.

relative frequency distribution

lists the proportion of occurrences of each category of data

Classes

the categories by which data are grouped

class width

the difference between consecutive lower class limits.

What does it mean if a statistic is​ resistant?

Extreme values​ (very large or​ small) relative to the data do not affect its value substantially.

A histogram of a set of data indicates that the distribution of the data is skewed right. Which measure of central tendency will likely be​ larger, the mean or the​ median? Why?

The mean will likely be larger because the extreme values in the right tail tend to pull the mean in the direction of the tail.

True or​ False: A data set will always have exactly one mode.

false

Why is the median​ resistant, but the mean is​ not?

The mean is not resistant because when data are​ skewed, there are extreme values in the​ tail, which tend to pull the mean in the direction of the tail. The median is resistant because the median of a variable is the value that lies in the middle of the data when arranged in ascending order and does not depend on the extreme values of the data.

The standard deviation is used in conjunction with the

mean to numerically describe distributions that are bell shaped

Mean

measures the center of the​ distribution

standard deviation

measures the spread of the distribution.

z-score

a measure of how many standard deviations you are away from the mean

stratified sampling

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

Determine whether the following statement is true or false. Explain.

Inferences based on voluntary response samples are generally not reliable.

​True, because it is often the case that the individuals who volunteer do not accurately represent the population.

Determine whether the following statement is true or false. Explain.

When obtaining a stratified​ sample, the number of individuals included within each stratum must be equal.

Choose the correct answer below.

False. Within stratified​ samples, the number of individuals sampled from each stratum should be proportional to the size of the strata in the population.