Introduction

Is the numerical value given a population parameter or a sample statistic? The average math score for all seniors who took the ACT was 20.7

20.7 is a population parameter because it is based on the scores for all seniors who took the ACT, which is the population.

Is the numerical value given a population parameter or a sample statistic? In a survey of high school seniors, 68% said they planned on attending college.

68% is a sample statistic because it is a description of a sample of high school seniors, since it would be impossible to survey every high school senior.

Is the numerical value given a population parameter or a sample statistic? The average grade on the final in your statistics class was an 82%

82% is a population parameter because it is based on the grades of all students in your statistics class.

Usually both of these branches of statistics are used in conjunction within the same statistical study. A common scenario in statistics is as follows:

A large population is to be studied. A sample is chosen that represents the population. Descriptive statistics are used to gather, sort, summarize, and present the information about the sample. Inferential statistics are used to estimate the population parameter from the sample statistics.

Parameter

A numerical description of a particular population characteristic. -the numbers that describe a population -parameter is a fixed number, often it is impossible or impractical to determine it precisely -best we can do is to estimate a population's true parameter. EX Suppose it is true that 65%65% of all Americans own a computer. Then 65%65% is a population parameter.

Sample

A subset of the population from which data are collected. That is, the sample is a group from within the population. When the parameter cannot be determined, a subset of the population, called a sample, is chosen -population must be represented well so the results of the study are meaningful

how do you decide if it is a a population parameter or a sample statistic?

As a general rule, first consider whether each statement refers to a sample or a population. To be a population parameter, it must describe ALL members being studied and not a portion of them.

Data

Information, in particular, information prepared for a study. -time sensitive -may not be practical for time frame or impossible -the information gathered -variety of forms including counts, measurements, or observations -If the population is small enough, data may be obtained from every member

Identify the population and sample. A survey of 1246 female college students in the U.S. showed that 96% own a computer.

Population: All female college students in the U.S. Sample: The 1246 female college students in the U.S. that were surveyed.

Identify the population and sample. A researcher randomly selects 20 males for a study of how one's diet affects blood pressure.

Population: All males. Sample: The 20 males selected.

What are some possible inferences that can be drawn from these statistics? In a sample of football games, the average number of times the quarterback was sacked is two times per game.

Possible inferences that can be drawn are if the offensive line is doing their job, the quality of the quarterback, and if the receivers are open.

determine whether the statement describes a population or a sample. The final exam scores in your math class

Recalling the definitions for population and sample, we know that the population is a particular group of interest and a sample is a subset of the population from which data are collected. In this case, we are looking at all of the final exam scores in your math class. This is the group of interest; and therefore, the statement describes a population.

determine whether the statement describes a population parameter or a sample statistic. 71%71% of all seniors at your school reside off campus.

Recalling the definitions for population parameter and sample statistic, we know that a parameter is a numerical description of a particular population characteristic and a statistic is the actual numerical description of a particular sample characteristic. Therefore, first consider whether the statement refers to a sample or a population. To be a population parameter, it must describe all members being studied, not just a portion of them. In this case, we are looking at the percentage of all the seniors at your school. This is the group of interest, and therefore, the statement describes a population parameter.

Sample Statistic

The actual numerical descriptions of a particular sample characteristic. -A number that describes a characteristic of a sample EX research group wants to know the percentage of college students that do laundry on a weekly basis. If 100 college students are chosen for the study, and 42% do laundry on a weekly basis, then the population would be all college students, and the 100 students chosen are the sample. The sample statistic would be 42% of students.

Population

The particular group of interest - A statistical study centers upon consists of all persons or things being studied - entire group of ____ *can be non-human (animals in a shelter)

Descriptive Statistics

This branch of statistics, as a science, gathers, sorts, summarizes, and displays the data. -involves the raw data, as well as the graphs, tables, numerical summaries, etc., used to describe these data -refer to the sample data without making any assumptions about the population from which the data was drawn. "just the facts" EX if you wanted to know the average age of fast food employees, descriptive statistics would involve gathering the ages of a sample of employees, as well as calculating and reporting the average age of that sample.

Inferential Statistics

This branch of statistics, as a science, involves using descriptive statistics to estimate population parameters. -interpretation of the information collected -typically conclusions about some hypothesis -accuracy of this inference is dependent upon how well our sample represents our population. EX If in our previous example of fast food employees, we calculated the average age of our sample to be 20 years old, then we could infer from this information that the average age of fast food employees nationally is 20 years old.

Identify the descriptive statistics in the following statement. What are some possible inferences that can be drawn from In a sample of football games, the average number of times the quarterback was sacked is two times per game.

Two sacks per game is a descriptive statistic

census

When data is obtained from every member of the population.

Identify the population being studied. The heights of 14 out of the 24 cucumber plants at Mr. Lonardo's greenhouse.

all cucumber plants at Mr. Lonardo's greenhouse.

If an instructor wants to know the number of statistics students with red hair, the population to be studied is

all statistics students.

If a software company wants to know the percentage of teenagers that own a personal computer, the population is

all teenagers.

The singular form of data is

datum

Determine whether the statement describes a descriptive or inferential statistic. The average price of a car at the new car dealership in town is $28,200

descriptive

Determine whether the statement describes a descriptive or inferential statistic. A recent poll of 3343 luxury car owners in West Virginia showed that the average price of a luxury car in the U.S. is $33,800

inferential statistic

statistics

is to provide information so that informed decisions can be made The science of gathering, describing, and analyzing data. OR The actual numerical descriptions of sample data.

test until destruction

light bulbs: how long till burn out cars: crash test

Determine whether the statement describes a population or a sample. The types of cars of all the professors at the local college.

population

Determine if the numerical value describes a population parameter or a sample statistic. 58% of all instructors at your school teach 2 or more classes.

population parameter *To be a population parameter, it must describe all members being studied, not just a portion of them.

Identify the population being studied and the sample chosen. The number of hours a group of 4 children in Mrs. Smith's kindergarten class play outside in a day.

population: all students in Smith's kindergarten class sample: a group of 4 children in Mrs. Smith's kindergarten class

Determine whether the statement describes a population or a sample. The heights of 6 out of the 29 tomato plants at Mr. Lonardo's greenhouse.

sample

Determine if the numerical value describes a parameter or a statistic. A recent poll of 2181 students showed that the average number of hours they study per week is 9.5

sample statistic

Determine if the numerical value describes a parameter or a statistic. A recent poll of 3810 students showed that the average number of hours they study per week is 10.1

sample statistice

Identify the sample chosen for the study. The number of times 11 out of 28 students on your floor order Chinese in a week.

sample: 11 students on your floor