Statistical Reasoning

Average cost of an airline meal

U.S. children who have high cholesterol

Average amount spent for a Father’s Day gift

Population ◦ The large, more general group from which the

sample group is gathered

Sample ◦ The specific group being studied

Population parameters ◦ The study (topic) that we wish to discover for the

entire group (population)

Sample statistics◦ The study (topic) that actually characterizes the

small group (sample)

A research team determines the average height and weight of U. S. college football quarterbacks by gathering data from 10 colleges in the South.

Population = all U.S. college football quarterbacks

Sample = all quarterbacks from the 10 Southern colleges

Population parameters = average heights and weights of all U.S. college football quarterbacks

Sample statistics = average heights and weights of the quarterbacks from the 10 Southern colleges

There are four ways to choose a sample:◦ Random sampling

◦ Systematic sampling

◦ Convenience sampling

◦ Stratified sampling

Choosing the people or things “any old way we want to do it”

Example: Draw names out of a hat

Example: Get names from a list

Example: Nursing supervisors are selected to determine yearly salaries

A “math” method is used to select the sample (look for a 5th, 7th, or similar number)

Example: Number each subject in the population and select every “nth” person (every 4th person, every 10th person, etc.)Example: Every 7th customer entering Cleveland Mall is asked to select his or her favorite storeExample: Every 100th hamburger made is checked to determine its fat content

Like the convenience store idea, the sample is selected because the people or things happen to be at the right place at the right time

Example: ask people in a local mall

Example: ask people in a classroom

Divide population into groups according to some characteristic – then make your sample by “picking some from each group”

Example: Get opinions at CCC from first-year students and second-year students

Example: Mail carriers are grouped by gender and according to whether they walk or ride on their routes. Ten selected from each group to see if they have ever been bitten by a dog

Observational study◦ Researchers simply “look at / watch / observe” the

sample without interfering or imposing conditions on the sample

Experiment study◦ Researchers apply a condition or a treatment to part

of the sample (or all of the sample) to see if that condition / treatment has any affects on the study

Example: Data collected on ages and incomes of motorcycle owners to see if otorcycle owners are getting older and richer

Researcher stood at busy intersection to see if color of car that a person drives is related to running red lights

Divide Va Tech students into two groups to do “sit up” exercises

One group told “do your best”

Other group told “ increase number of sit ups by 10% more each day”

Subjects assigned to a group. Each group placed on low fat, high fish, combo, or regular diet. Blood pressures compared after 6 months to see if diet has effect on BP.

Qualitative Data◦ Deals with descriptions

◦ Can be observed and is “non-numerical”

Quantitative Data◦ Deals with numbers

◦ Can be measured and/or counted

Marital status of hospital nurses

Colors of cars in CCC parking lotA person rating a movie (four stars, three stars, etc.)

Time it takes to run a kilometer

Weight of lobsters in a tank at a restaurant

Ounces of fruit in a smoothie

Seating capacity of football stadium

Age of people living in nursing home