MTH 139 chapter 1

designing a statistical study

1. identify the variables of interest (the focus) and the population of the study 2. develop a detailed plan for collecting data. if you use a sample, make sure the sample is representative of the population 3. collect the data 4. describe the data, using descriptive stats techniques 5. interpret the data and make decision about the population using inferential statistics 6. identify any possible errors

example:

614 small business owners in the US were asked whether they thought their company facebook presence was valuable. 258 of the 614 says yes. which is the population and which us the sample? population- all small business owners in the United States sample- 258 said yes, 356 said no

example- a recent survey of approximately 400,000 employers reported that the average starting salary for marketing majors is $53,400.

Sample statistic because the average of $53,400 is based on a subset of the population

sampling

a count or measurement of a part of the population, more common in statistical studies

census

a count or measurement of an entire population **costly and difficult to perform**

parameter

a numerical description of a POPULATION charactersitic - CONSTANT FOR A POPULATION

statistic

a numerical description of a SAMPLE characteristic - SAMPLE STATISTIC CAN DIFFER FROM SAMPLE TO SAMPLE

what is the difference between a parameter and a statistic?

a parameter is a numerical description of a population characteristic a statistic is a numerical description of a sample characteristic

randomization

a process of randomly assigning subjects to different treatment groups

experiment

a researcher deliberately applies a treatment before observing the responses

observational study

a researcher does not influence the responses

how is a sample related to a population?

a sample is a subset of a population

sample

a subset, or part, of a populations

random sampling

an appropriate method of collecting data

a statistical study can be classified as either-

an observational study or an experiment

interval level of measurement

can be ordered, and meaningful differences between data entries can be calculated. at the interval level, a zero entry represents a a position on a scale , the entry is not an inherent zero.

population

collection of ALL outcomes, responses, measurements, or counts that are of interest

qualitative data

consist of attributes, labels, or nonnumerical entries

quantitative data

consist of numerical measurements or counts

data

consists of information coming from observations, counts, measurements, or responses

what are 3 key elements of a well-designed experiment?

control, randomization, and replication

random sample

every member of the population has an equal chance of being selected

true or false: a population is the collection of some outcomes, responses, measurements, or counts that are of interest.

false- a population is the collection of ALL outcomes, responses, measurements, or counts that are of interest

true or false: a statistic is a numerical value that describes a population characteristic.

false- a statistic is a numerical value that describes a sample characteristic.

t or f- data at the ratio level cannot be put in order

false- data at the ratio level is put in order.

t or f- more types of calculations can be preformed with data at the nominal level than with data at the interval level

false- more types of data can be performed with data at the interval level than at the nominal level

t or f- data at the ordinal level are quantitative only

false- ordinal level can be quantitative and qualitative

name each level of measurement for which data can be qualitative-

nominal and ordinal

name each level of measurement for which data can be quantitative-

ordinal, interval, and ratio

2 types of data sets

population and samples

example- the freshman class at a university has an average SAT math score of 514

population parameter because the average SAT math score of 514 is based on the entire freshman class

pop or samp: the revenue to each of the 30 companies in the Dow Jones Industrial Average

population- because it is a collection of the revenues of the companies in the Dow Jones Industrial Average

the final score of each golfer in a tournament.

population- it is a collection of all the golfers' scores in the tournament.

nominal level of measurement

qualitative only- this means data is categorized using names, labels, or qualities

ordinal level of measurement

qualitative or quantitative- data at this level can be arranged in order, or ranked, but differences between data entries are not meaningful

qual or quan- responses on an opinion poll

qualitative- because the poll responses are attributes

qual or quan- eye colors of models

qualitative- eye colors are attributes

qual or quan- heights of hot air balloons

quantitative- balloon heights are numerical measurements

qual or quan- weights of infants at a hospital

quantitative- infant weights are numerical measurements

simple random sample

sample in which every possible sample of the same size has the same chance of being selected

pop or samp: the cholesterol levels of 20 patients in a hospital with 100 patients

sample- the collection of 20 patients is a subset of the population of 100 patients at the hospital.

pop or samp: a survey of 500 spectators from a stadium with 42,000 spectators

sample- the collection of the 500 spectators is a subset of the population pf 42,000 spectators at the stadium

ratio level of measurement

similar to interval, with added property that a zero entry is an inherent zero. a ratio of two sets of data entries can be formed so that one data entry can be meaningfully expressed as a multiple of another.

statistics is derived from the latin word

status (meaning the state)

descriptive statistics

the branch of statistics that involves the organization, summarization, and display of data

inferential statistics

the branch of statistics that involves using a sample to draw conclusions about a population (probability)

replication

the repetition of an experiment under the same or similar conditions

statistics

the science of collecting, organizing, analyzing, and interpreting data in order to make decisions

example- which part represents the descriptive branch: in a sample of Wall Street analysts, the percentage who incorrectly forecasted high-tech earnings in a recent year was 44%

the statement "the percentage of Wall Street analysts who incorrectly forecasted high-tech earnings in a recent year was 44%" is descriptive

blinding

the subjects do not know whether they are receiving a treatment or a placebo

true or false: it is impossible for the Censes Bureau to obtain all the census data about the population of the United States.

true

confounding variable

when an experimenter cannot tell the difference between the effects of different factors on the variable