Statistics: Quiz 1

What kind of experiment is the following: researchers observe subjects and measure variables interest without assigning treatments to the subject

Observational study: no attempt to influence outcomes

Identify the population and sample: During the Super Bowl game, a marketing company emails a survey to 6000 randomly selected households about effectiveness of the commercials. 4000 individuals respond, some indicating they did not watch the Super Bowl.

Population: all house holds with access to super bowl Sample: 4000 individuals responded

Identify the following variables as quantitative (measurement) or qualitative (categorical). If quantitative, identify as discrete or continuous. Student identification numbers (S0#s at SEMO)

Qualitative

Social Security Number

Qualitative, nominal

What kind of experiment is the following: Researchers randomly apply treatments to experimental units (people, animals, plots of land, etc.) and then proceed to observe the effects of the treatment on the experimental units.

Randomized Experiment -randomly divide into 2 groups 1.) treatment 2.) no treatment treatment: medicine, training program

sample frame

-A list of individuals or items from which the sample is taken. -Ideally the individuals or items in the sampling frame are the same as the individuals or items in the population. -If the population is all students enrolled in a course at Southeast, it's possible to compile a list of all Southeast students for the sampling frame. -If the population is all hunters in Missouri, it's possible to compile a list of all individuals with a Missouri hunting permit. Landowners do not need a permit to hunt on their own property, so they may not have a hunting permit. In this case the sampling frame may not be identical to the intended population.

Voluntary response sampling

-post a survey and allow respondents to choose whether or not they respond

types of sample

-simple random sample -stratified sample -cluster sample -systematic sample -convenience sample

stratified random sample

1.Divide the population into groups of similar individuals, called strata. In practice, the strata are chosen from the sampling frame. Ideally the sampling frame is the same, or very close to being the same, as the population. 2.Choose a separate simple random sample in each stratum. 3.Combine these simple random samples to form the full sample.

Find relative frequency of sale price/item: Frequency no of items: $1-5 8 $6-10 6 $11-15 4 Total: 32

8/32=.25=25%

Sampling Bias

A sample is collected from a population and some members of the population are not as likely to be chosen as other members. -undercoverage: leave out groups of people

Bias

A statistic is biased if it is calculated in such a way that it systematically under estimates or over estimates the population parameter

Systematic sampling

A systematic sample is obtained by selecting every k th individual from the population. The first individual selected is a random number between 1 and k.

Cluster Sampling

Cluster sampling involves the selection of all members in randomly selected groups, or clusters. 1.Divide the population into clusters. 2.Randomly choose clusters. 3.All subjects in the chosen clusters make up the sample.

Quantitative or Measurement Variable

Numeric value that represents count or measurement, height, weight, GPA

What sample is this: Example: Undergraduate college students are divided by credit hours completed—at most 30 hours, 31-60 hours, 61 to 90 hours, at least 90 hours. 50 students in each group are randomly selected and given a survey about relevant issues. It's okay if strata are of unequal size. If more freshmen (at most 30 hours) are enrolled, you may want that strata to be larger than the other three strata.

Stratified random Sample

what kind of sampling is: Example: Every 200th product coming off an assembly line is pulled and weighed to see if the products are the correct weight.

Systematic sampling

inferential statistics

Use descriptive statistics from sample to reach conclusions about populations

cumalative frequency

add right side till you get down the the number they asked about on the left

Is convenience sampling likely to be a representative sample?

almost never

paramter

calculation from a population mean of population, M (but curvy M)

Statistic

calculation from a sample, (X with line above it)

Qualitative or

categorical data

what kind of sample is this: Example—The clusters could be the ER in each hospital in a city. Randomly choose 5 hospitals and survey all the ER triage nurses in the 5 hospitals about certain practices

cluster sampling

what kind of sample is: Example: Stand outside a store and ask recent customers about a product just purchased.

convenience sampling

what kind of sample is: Example: Suppose as a freshman, you are unhappy with the method of registration at Southeast and decide to issue a formal complaint. To gather support, you ask the opinions of students that live on your floor that are also freshmen.

convenience sampling

discrete data

countable data

Discrete variable

countable usually whole number

response variable

dependent variable: changes as result of explanatory variable

Convenience Sampling

do whats easy to collect data

Population

entire group being studied

What are the two variables

explanatory and response

How do you find relative frequency

freq/total

Frequency table to histogram: what side does relative frequency label go on and ranges

frequency on left side and ranges on bottom

explanatory variable

independent variable: causing the change

Interval or ratio: (temp) C and F

interval

A quantitative variable may be

interval or ratio

nominal variable

just a label, name only, gender, ethnicity, etc.

ordinal variable

label with a clear order; good, ok, bad

Descriptive statistics

look at sample, draw graph, look at table, do calculations

quantitative or

measurement data

interval variable

no true 0 starting point, find differences (subtract), temp in F or C

A qualitative variable may be

nominal or ordinal

Continuous variable

not countable, between any 2 values is another value weight

What kind of experiment is the following: -find 100 women age 30 of which 50 have been smoking a pack a day for 10 years when the other 50 have been smoke free for 10 years -measure lung capacity for each of the 100 women -analyze, interpret, and draw conclusions from data

observational study: explanatory- smoking or not smoking response variable- lung capacity

Statistic or parameter: 20% of college As students are women

parameter

Identify if the following data represents a parameter or statistic. 42% of the governors of the 50 United States are Democrats.

paramter

Non response bias and how can we improve this?

people dont respond, represent certain groups we can do call backs or have incentives

Identify the population and sample: A political scientist randomly selects 25 of the 100 senators currently serving in Congress, then finds the lengths of time that they have served.

population: 100 senators sample: 25 selected senators

Identify the following variables as quantitative (measurement) or qualitative (categorical). If quantitative, identify as discrete or continuous. Eye color

qualitative

Grades in a course: A, B, C, D, F

qualitative, ordinal

variable

quality or quantity being studied

what can be discrete or continuous

quantitative

Whats discrete or continuous

quantitative variable

Identify the following variables as quantitative (measurement) or qualitative (categorical). If quantitative, identify as discrete or continuous. High temperature in Cape Girardeau for each day in July

quantitative, continuous

Identify the following variables as quantitative (measurement) or qualitative (categorical). If quantitative, identify as discrete or continuous. Weight of all football players on roster at Southeast

quantitative, continuous

temperature of an August day in degrees Fahrenheit

quantitative, continuous, interval

weight of football players on SEMO roster

quantitative, continuous, ratio

Identify the following variables as quantitative (measurement) or qualitative (categorical). If quantitative, identify as discrete or continuous. The years of cicada emergence: 1936, 1953, 1970, 1987, 2004

quantitative, discrete

Year of graduation from high school of all students currently at Southeast

quantitative, discrete, interval

Yearly salary of employees at Southeast

quantitative, discrete, ratio

interval or ratio: age in years

ratio

interval or ratio: weight in pounds

ratio

Qualitative or Categorical Variables

represents quality or characteristic, label, gender, ethnicity, grade level

Qualitative

result of categorizing or describing attributes of a population

quantitative

result of counting or measuring attributes of a population always numerical data

continuous data

result of measuring as long as measuring device is precise; between two values is another value

Voluntary response sample

sample members are self-selected and likely to be a biased sample

what kind of sample is: Given a population of size N, each sample of size n has an equally likely chance of being chosen.

simple random sample: like drawing names from a hat

Identify if the following data represents a parameter or statistic. A news source reports the average amount of time watching television is 4.6 hours per day.

statistic

Identify if the following data represents a parameter or statistic. A sample of households is selected and the average (mean) number of people per household is 2.58. (U.S. Census Bureau)

statistic

sample

subset of population

ratio variable

true 0 starting point, compare with ratios (percents), also subtract weight of newborn

Why use stratified sampling?

•Also find individual estimates for each stratum. •If the variables are more consistent within each stratum than within the population, stratified sample produces more accurate estimates of the population variables. •Depending on location of strata, stratified sampling may be cheaper. •Allows use of different interviewers in each strata.

Advantages of Cluster Sampling

•Only a list of clusters in needed, not a list of each individual or item. •Cheaper to survey everyone in several locations than a few people in many locations.