ST 311 Exam 1

Population

entire group of items/individuals that we want information about

Sample

smaller group, part of a population, who we actually examine

What letter represents sample size?

n

Parameter

(numerical) summary of population (typically unknown)

Statistic

(numerical) summary of a variable for a sample (used to estimate parameter)

Voluntary response sample

only those people who volunteer are included in the sample

Convenience sample

the most convenient (readily available) group in the considered sample

Bad sampling methods

Voluntary response sample and convenience sample

Good sampling methods

Simple random sample (SRS), systematic sampling, stratified random sample, cluster sample

Simple Random Sample (SRS)

pick individuals completely at random to be in the sample

Systematic sampling

select some starting point and then select every kth element in the population

Stratified random sampling

the population is first divided into nonoverlapping groups (strata) and a simple random sample is selected from within each group

Cluster sample

the population is first divided into nonoverlapping groups (cluster) and a simple random sample of clusters is selected: all individuals in the selected clusters are included in the sample

Stratified vs. Cluster Sampling

Stratified: choosing within each group

Cluster: choose a group itself

Bias

tendency for a sample to differ from the corresponding population

Types of bias

Bad sampling frame, under coverage, non-response bias, response bias, wording & order

Bad Sampling Frame

it’s hard to get a list of who is in the population

Undercoverage

the sampling frame excludes some parts of the population

Non-response Bias

a subset of the sample cannot be contacted or does not respond

Response Bias

participants respond differently from how they truly feel

Wording & Order

the way the questions are worded or ordered may by leading to have the individual answer a certain way

Randomized Methods

completely randomized design, randomized block design, matched pairs design

Completely Randomized Design

we randomly assign subjects to the different treatments

Randomized Block Design

we split the subjects into groups (blocks) based on some lurking (or block) variable. Then we randomly assign the treatments within each block

Matched Pairs Design

we pair individuals up based on similarity and then randomly choose one person in each pair to get one treatment and the other gets the other treatment

Center

mean, median, and mode

Spread

standard deviation, IQR, and range

Consistency equals (=)

spread

Mean and IQR are…

resistant to outliers

Mean and Standard Deviation are best if…

distribution is relatively normal and there are no outliers

Quantitative Data

histograms, box plots

What does quantitative data show?

shows the distribution of the data

Qualitative Data

pie charts, bar charts

What does qualitative data show?

Separated categories and shows the frequencies and shows the frequency or proportion of each category

The Normal Distribution - look

symmetric and bell-shaped

The Normal Distribution - characterized by…

Characterized by its mean, which is at the center of the distribution, and its standard deviation

X - normal

(μ, δ) means X follows a normal distribution with mean μ and standard deviation δ

Z - normal

(0,1) is the “standard normal” distribution

Standard Normal

(0,1) or Z - Normal

Standardized score or z-score

the distance between an observation and the mean, measured in terms of number of standard deviations

Empirical Rule

Used to estimate normal distribution probabilities

• 95% of the data is within 2 standard deviations of the mean

What does Z > 2 mean?

the observation is unusual

What are the 4 conditions to binomial random variables

1. Fixed number of trials (sample size n is constant)

2. Each trial is independent of the others

3. Two possible outcomes: “Success” and “Failure”

   1. Probability of a success p is constant

Standard Error

the standard deviation of its sampling distribution

Sampling Variability

the variation in sample statistics that results from selecting different random samples

Parent Population

X is a random variable with mean μₓ and standard deviation δₓ

Central Limit Theorem (CLT)

if either (1) the parent population is normal or (2) n ≥ 30

p hat

x / n (x=# of successes, n=sample size)

Expected Values of X

E(X) = μₓ = np

Standard Deviation of X

δₓ = √npq where q = 1-p