STAT 113: EXAM 2 STUDY GUIDE COLIN REIMER DAWSON, FALL 2015 (1) - - PDF document

STAT 113: EXAM 2 STUDY GUIDE

COLIN REIMER DAWSON, FALL 2015

(1) Chapter 3: Inference Foundations / Bootstrap Confidence Intervals 3.1 Sampling Distributions. You should be able to

• Recognize and explain the difference between a popula-

tion and a sample, and between a parameter and a statis- tic.

• Understand how to find good point estimates of parame-

ters using a sample.

• Understand what a sampling distribution is, what the

cases are in a sampling distribution, and what the in- dividual values in a sampling distribution represent.

• Understand what a standard error is, how it relates to

standard deviation, and how it contrasts with variability

• f individual cases in a sample.
• Recognize where a sampling distribution is typically cen-

tered.

• Use the ±2SE rule when appropriate to recognize where

most sample statistics fall in a sampling distribution.

• Recognize when the ±2SE rule is and isn’t appropriate.
• Visually estimate standard error from a dot plot or his-

togram of a sampling distribution / bootstrap distribution / randomization distribution

• Distinguish between sample size and number of samples

in a simulated sampling distribution.

• Recognize the effect of sample size on variability of sample

statistics. 3.2 Confidence Intervals. You should be able to

• Interpret what a margin of error is telling us.

Date: November 16, 2015.

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2 COLIN REIMER DAWSON, FALL 2015

• Recognize the relationship between standard error of a

sampling distribution and margin of error of an estimate.

• Construct a confidence interval from a point estimate and

either a margin of error or a standard error.

• Interpret a confidence interval (what is likely to be within

it?)

• Interpret the confidence level (what happens 95% or 99%
• f the time?)
• Recognize and avoid common misinterpretations of the

confidence interval. 3.3 Boostrap Confidence Intervals. You should be able to

• Understand what it means to “bootstrap resample” from

a sample.

• Recognize what the values in a bootstrap distribution rep-

resent.

• Understand where a bootstrap distribution is centered
• Understand the role of the standard deviation of the boot-

strap distribution.

• Construct a 95% confidence interval from a point estimate

and a bootstrap standard error. 3.4 Boostrap Confidence Intervals Using Percentiles. You should be able to

• Identify which quantiles of a bootstrap distribution are

needed for a particular confidence level

• Identify what confidence level is associated with particu-

lar quantiles of a bootstrap distribution (2) Chapter 4: Hypothesis Tests Using Randomization 4.1 Hypothesis Testing Basics. You should be able to

• Identify when a hypothesis test is called for (vs. a confi-

dence interval, vs. no need for inference)

• Construct null and alternative hypotheses, in both words

and statements about population parameters, from a re- search question.

• Recognize the distinction between a sample having a par-

ticular mean/proportion/difference/correlation and the pop- ulation having the same.

STAT 113: EXAM 2 STUDY GUIDE 3

• Recognize which sample statistics provide the strongest

evidence for a particular hypothesis.

• Interpret what it means that a finding is statistically sig-

nificant. 4.2 P-values. You should be able to

• Understand the role of a randomization distribution in

hypothesis testing.

• Recognize what the values in a randomization distribution

represent

• Recognize what is assumed when generating a random-

ization distribution.

• Recognize what the center of a randomization distribution

is in the context of the hypothesis test.

• Understand what a P-value is, as a proportion (What

goes in the numerator? What goes in the denominator?)

• Understand which cases in the randomization distribution

to count toward the P-value in a one-tailed or two-tailed test.

• Understand the tradeoff between flexibility and statistical

power when deciding between a one- and two-tailed test. 4.3 Statistical Significance and Statistical Errors. You should be able to

• Understand the role of the significance level (α) in decid-

ing whether a result is statistically significant.

• Understand what Type I Errors / False Discoveries are,

and how the likelihood that they occur is related to the significance level, α.

• Understand what a Type II Error / Missed Discovery is,

and how its likelihood is related to the significance level, α, as well as to the sample size. 4.4 Constructing Randomization Distributions for Different Hypothe-

• ses. You should be able to
• Understand / describe the process of generating a ran-

domization distribution to test whether a population pro- portion is equal to a particular null value.

4 COLIN REIMER DAWSON, FALL 2015

• Understand / describe how to create a randomization dis-

tribution from a bootstrap distribution to test whether a population mean is equal to a particular null value.

• Understand / describe a process to generate a randomiza-

tion distribution to test whether two subpopulations have different rates (proportions) of a particular categorical re- sponse variable.

• Understand / describe a process to generate a randomiza-

tion distribution to test whether two subpopulations have different mean levels of a particular quantitative response variable.

• Understand / describe a process to generate a random-

ization distribution to test whether two quantitative vari- ables are correlated in a population. 4.5 Tests and Confidence Intervals. You should be able to

• Interpret confidence intervals in terms of possible null hy-

potheses about a population parameter.

• Use a confidence interval to make a binary decision at the

approporiate significance level about whether a particular null hypothesis value can be rejected. (3) Chapter 5. Using a Normal Distribution 5.1 Normal Distributions. You should be able to

• Understand the relationship between a proportion of cases

in a simulated distribution, and the area under a density curve in a theoretical distribution.

• Estimate tail proportions visually by looking at a density

graph

• Estimate quantiles visually using a density graph
• Understand how to combine tail proportions to get pro-

portions in intervals.

• Recognize what happens to a distribution of a variable

when we convert its values to z-scores.

• Understand how the area/proportion past a z score in a

Standard Normal relates to the area past a value that has that z score in a different (non-standard) Normal. 5.2 Confidence Intervals and P-values Using Normal Distributions. You should be able to

STAT 113: EXAM 2 STUDY GUIDE 5

• Recognize when it would be appropriate to use a Normal

approximation for a bootstrap or randomization distribu- tion.

• Identify the approximate z-scores corresponding to some

commonly used Normal quantiles (e.g., 0.005, 0.025, 0.05, 0.95, 0.975, 0.995).

• Use these z-scores, together with a point estimate and a

standard error of a sample statistic, to create 90%, 95% and 99% confidence intervals

• Understand / describe what we would need to do to get

a confidence interval at some other confidence level.

• Understand how to find the parameters (mean and stan-

dard deviation) to use for a non-standard Normal approx- imation to a randomization distribution

• Understand / describe what we would need to do to get a

P-value from such a (non-standard) Normal approxima- tion to a randomization distribution.

• Convert an observed statistic into a z-score using an ap-

propriate mean and standard deviation, based on proper- ties of a randomization distribution.

• Use such a z-score to give a rough estimate of a P-value

(“rough” meaning “Is it less than 0.01? Between 0.01 and 0.05? Between 0.05 and 0.1? Greater than 0.1?”) (4) Chapter 6. Tests and Intervals Using Normal Theory 6.1-6.3 Inference about a Proportion. You should be able to

• Recognize when it is and is not appropriate to use a Nor-

mal to approximate a distribution of sample proportions.

• Decide what choice of p to use in what contexts when

computing the standard error for a proportion.

• Use the theoretical standard error for a proportion (cal-

culated using the appropriate p), together with critical Z∗ values, to find the margin of error for a 90, 95 or 99% confidence interval for a population proportion.

• Recognize what it would take to find critical Z∗ values for
• ther confidence levels.
• Use the theoretical standard error for a proportion (cal-

culated using the appropriate p), together with a null hy- pothesis, to convert a sample proportion into a Z statistic,

6 COLIN REIMER DAWSON, FALL 2015

and give a rough estimate for a P-value (“rough” meaning “Is it less than 0.01? Between 0.01 and 0.05? Between 0.05 and 0.1? Greater than 0.1?”).

• Interpret confidence intervals and P-values in terms of

what they say about population proportions. 6.4-6.6 Inference about a Mean. You should be able to

• Recognize when it is and is not appropriate to use a Nor-

mal to approximate to a distribution of sample means.

• Explain how population variability and sample size affect

the distribution of sample means.

• Understand the difference between a t-distribution and a

standard Normal distribution, and understand when and why we need to get quantiles and tail proportions using a t rather than a standard Normal.

• Recognize the effect of not knowing the population stan-

dard deviation on the width of a confidence interval, and

• n P-values.
• Use the estimated standard error for a mean together with

critical T ∗ values to find the margin of error for a 90, 95

• r 99% confidence interval.
• Use the estimated standard error for a mean together with

a null hypothesis to convert a sample mean into a T statis- tic, and understand where the P-value would fall in com- parison to that for an identical Z statistic.

• Interpret confidence intervals and P-values in terms of

what they say about population means. 6.7-6.9 Inference about a Difference of Proportions. You should be able to

• Recognize when it is and is not appropriate to use a Nor-

mal to approximate a distribution of differences between two proportions.

• Understand why the standard error of a difference is what

it is.

• Decide what choices of p to use in what context when

computing the standard error for a difference in propor- tions.

• Use the theoretical standard error for a difference in pro-

portions (calculated using the appropriate choice(s) for

STAT 113: EXAM 2 STUDY GUIDE 7

p(s)), together with critical Z∗ values, to find the mar- gin of error for a 90, 95 or 99% confidence interval for a difference of population proportions.

• Use the theoretical standard error for a proportion (cal-

culated using the appropriate p), together with a null hy- pothesis, to convert a difference of sample proportions into a Z statistic, and give a rough estimate for a P-value (“rough” meaning “Is it less than 0.01? Between 0.01 and 0.05? Between 0.05 and 0.1? Greater than 0.1?”).

• Interpret confidence intervals and P-values in terms of

what they say about differences of population propor- tions. 6.8-6.13 Inference about a Difference of Means / Mean of Differences. You should be able to

• Recognize when it is and is not appropriate to use a Nor-

mal to approximate a distribution of differences between two means.

• Understand why the standard error of a difference is what

it is.

• Identify the appropriate distributions to use to get crit-

ical values and P-values for confidence intervals and hy- pothesis tests, respectively, regarding differences between means.

• Interpret confidence intervals and P-values in terms of

what they say about differences of population means.

• Understand why we would decide to use a paired samples

design

• Understand the effect of using paired samples on confi-

dence intervals and P-values.

• State appropriate null and alternative hypotheses for paired

samples.

• Recognize the relationship between tests and intervals for

a mean difference and tests and intervals for a mean.