Chapter 9 Terminology : Sampling Distributions

Population Parameter
Sampling Distribution
(assume all from samples of size = n)
Single Sample Statistic
shape
any
If population is normal then distribution is normal (normal=gaussian=bellshaped)
or
for means, generally assumed normal if n>30
or
for proportions, generally assumed normal if np>10 AND nq>10
any
center
mean = u
or
proportion = p
Sampling Distribution for Means (mean of means; Note: plural) = u_{x̄} = u
or
Sampling Distribution for Proportions (mean of proportions; Note: plural) u_{p̂} = p
mean = x̄
or
proportion = p̂
spread
standard deviation of population mean = σ
or
no standard deviation of population proportion in AP Statistics, use IQR or range
Standard Error, SE = standard deviation in the sampling distribution for means, σ_{x̄} = σ/√n = s/√n
or
Standard Error, SE = standard deviation in the sampling distribution for proportions, σ_{p̂} = √(pq/n)
standard deviation of a sample mean = s
or
no standard deviation of sample proportion in AP Statistics, use IQR or range

sampling distribution :

of the sample mean, u_{x}

of the sample sum

of the number of success in a sample

of a sample proportion
 sample proportion as a type of mean

sample size versus population size
Central Limit Theorem
Point estimators :

biased versus unbiased : center : does statistic = parameter?

precision versus variability : spread : how much does statistic differ from parameter?

Standard Error of Distribution [average distance of centers away from the center of distribution] vs Standard Deviation [average distance of data away from center of data] has multiple uses and formulas.
Rare events and reasonably likely events
Chapter 10 Terminology : Introduction to Inference

reasonably likely event

rare event

proportion

confidence interval

significance test

level of confidence (capture rate)

margin of error

variation in sampling

statistical significance

condition (assumptions) for a test

null hypothesis and alternative hypothesis

test statistic

Pvalue

critical values

level of significance

Type I error and Type II error

power of a test

onesided test and twosided test

difference of two proportions

confidence interval

significance test

pooled estimate p̂

difference of two proportions from an experiment or observational study

significance test

confidence interval
Chapter 12 Terminology : Inference for Proportions in Populations

plausible population means

sampling distribution for s

confidence interval for a mean

using s as an estimate for σ

ttable

degrees of freedom

confidence level

capture rate

margin of error

ttest

tdistribution

significance test for a mean

statistical significance

fixedlevel testing

null hypothesis and alternative hypothesis

test statistic

level of significance

Pvalue

power

transforming to normality using logs and reciprocals

robustness of tprocedures

15/40 guideline for using tprocedures

independent random samples

random assignment of treatments to subjects

pooled versus unpooled sample variances

paired data

matched pairs design

repeated measures design

independent and dependent samples

mean difference
Chapter 11 Terminology : Inferences for Distributions (Means in Populations)
 test statistic
 significance test
 confidence interval
 degrees of freedom for inference
Chapter 13 Terminology : Inferences for Tables (ChiSquare Procedures in Categorical Data)
Flowchart courtesy of Bloomington Tutors [https://bloomingtontutors.com/blog/whentousetheztestversusttest]
Basically, it depends on four things:
 Whether we are working with a mean (for example, "37 students") or a proportion (e.g., "15% of all students").
 Whether or not we know the population standard deviation (s). In real life we usually don't, but statistics courses like to contrive problems where we do.
 Whether or not the population is normally distributed. This is mainly important when dealing with small sample sizes.
 The size of our sample. The magic number is usually 30  below that is considered a "small" sample, and 30 or above is considered "large". When the sample size is large, the central limit theorem tells us that we don't need to worry about whether or not the population is normally distributed.
When you're working on a statistics word problem, these are the things you need to look for.
 Proportion problems are never ttest problems  always use z!
 Proportions are always in terms of percentages among 2 options that add to 100%..."winner vs loser" or "like vs dislike"
 However, you need to check that n(p_{0}) and n(1p_{0}) are both greater than 10, where n is your sample size and p_{0} is your hypothesized population proportion. This is basically saying that the population proportions (for example, % male and % female) should both be large enough so they will be adequately represented in the sample.
Generally speaking, the problem will explicitly tell you if the population standard deviation is known  if they don't say, assume that it's unknown. The same goes for a normally distributed population  if they don't say "assume the population is normally distributed", or something to that effect, then do not just make up that assumption. Fortunately if the sample size is large enough, it doesn't matter!
Chapter 14 Terminology : Inference for Regression Lines

true regression line

line of means

conditional distribution of y given x

variability in x

variability in y at a given x

standard error in the slope, σ_{b1}

estimate of the standard error for the slope, s_{b1}

slope
Welcome Seniors to the Isle of Dr. Eville.
Rules to Escape the Isle of Dr. Evil

There is a 2nd Final Exam and you have just received a ZERO on it...verify the reality!

Complete the following tasks to receive an "X" on the 2nd Final Exam thereby Excusing yourself from its consequences and escaping Eville's domain.
Task 1  Random Award for Just Living

On TED, use GoogleMaps to find your house.
Show Dr. Eville and receive your due reward.
Task 2  Have you been Good Enough?

If you have any bathroom passes remaining, turn them in for a Random Reward, 1 per bathroom pass.
Task 3  Destroy all Juniors

On one of the computers is an existing login with a PowerPoint open.

Add a slide to the PowerPoint and create an AP Statistics Question for the next set of Juniors and include your name.

On the next new slide, write the solution to your AP Statistics Question and include your name.

Save the PowerPoint file and show Dr. Eville.
Task 4  Silence is Golden
Write on a class board your name, a number between 1 and 15 and your favorite "goodbye EHS" quote

The random "winning" student who can remain the quietest for the 10 minutes prior to 10 minutes before the bell will receive a piece of Sidewalk Chalk...
...and will be given a pass to write their quote on the concrete in front of the main doors.

[remember security videos are always being taken...and consequences for failure will not be tolerated]
Task 5  Stats Quizzes
Under Dr. Eville's AP Statistics course under RESOURCES tab
take the Practices Quizzes at this link
Task 6  Stay until the End
Ignore all other students in the hall...they are tempting but will lead you away from your "X"
Email Dr. Eville your ideas for future escape plans
...and don't wake up Dr. Eville until 10 minutes before the bell