# Stat 202 Objectives

From Sean_Carver

By the end of the course, students will be able to ...

## Contents

- 1 Chapter 1
- 2 Chapter 2
- 3 Chapter 3
- 4 Chapter 4
- 5 Chapter 5
- 6 Chapter 6
- 7 Chapters 7 & 8
- 8 Chapter 11
- 9 Chapter 12
- 10 Chapter 13 & 14 & 15
- 11 New Material for final
- 12 Chapter 15: Random Variables
- 13 Chapter 16: Probability Models
- 14 Chapter 17: Sampling Distributions Models
- 15 Chapter 18: Confidence Intervals for Proportions
- 16 Chapter 19: Testing Hypotheses about Proportions
- 17 Chapter 20: Inference About Means
- 18 Chapter 21: More about Tests and Intervals
- 19 Chapter 22: Comparing Groups
- 20 Chapter 23: Paired Samples and Blocks

## Chapter 1

- Given a data table and the story behind the data, identify the cases and list the variables.
- Identify a variable as either nominal, ordinal, identifier, binary, or quantitative.

## Chapter 2

- Define and report the distribution of a categorical variable.
- Be able to convert between frequency, relative frequency, and percent.
- Tell when two plots of categorical data show the same distribution.

## Chapter 3

- Define distribution of a quantitative variable.
- Create stem and leaf displays from data.
- Understand how histograms drawn with different bin widths can look different.
- Recognize when stem plots drawn with and without split stems are the same.
- Know to put gaps in stem plots when gaps exist in data.
- Tell from a histogram whether a distribution is symmetric or left or right skewed.
- Tell whether a histogram is uniform, unimodal, bimodal, or multimodal and why.
- Tell whether a histogram shows outliers, or gaps.
- Describe how to compute the median.
- Describe how to compute the mean.
- Describe how to compute the lower and upper quartiles and the interquartile range (IQR).
- Describe how to compute the standard deviation.
- For summary statistics, describe the difference between
*resistant to outliers*and*sensitive to outliers*. - Compute the 5-number summary of data.
- Given data, compute the value for a specific percentile.
- Given data, compute the percentile for a specific value.

## Chapter 4

- Identify the symmetry or left or right skew in boxplots.
- Comparing boxplots across groups, tell which groups have the greatest, and least, medians.
- Comparing boxplots across groups, tell which groups have the greatest, and least, interquartile range.

## Chapter 5

- Find mean and standard deviation, and other summary statistics, for a quantitative variable.
- Given the mean and standard deviation for the raw data, compute the z-score for particular data points.
- Given the mean and standard deviation for the raw data, compute the raw score for particular z-scores.
- Interpret a z-score as the number of standard deviations of a data point above the mean.
- Know that, after transforming data to z-scores, the mean of the z-scores is 0.
- Know that, after transforming data to z-scores, the standard deviation of the z-scores is 1.
- Given several Normal probability plots, identify which looks most Normal (it should will be obvious).
- Use the Normal calculator in StatCrunch to compute percentiles and related quantities.
- Know the parameters for the standard Normal model (mean 0, standard deviation 1).
- Know that if the data follow a Normal distribution, the z-scores follow a standard Normal distribution.
- Know that if the data do NOT follow a Normal distribution, the z-scores do NOT follow Normal distribution either, standard or otherwise, although mean of the z-scores is always 0 and the standard deviation is always 1.

## Chapter 6

- Know what it means for two variables to be
*associated,*(knowing the value of one variable tells you something about the value of the other that you would not know otherwise). - Be able to describe an association in terms of its form, strength, and direction.
- Be able to identify outliers for the relationship between the variables as possibly distinct from outliers in just one variable alone.
- Know the difference between explanatory variables and response variables, and which goes on which axis.
- Know how to draw a scatter plot.
- Know how to identify an association between two variables as linear, possibly with scatter.
- Know how to compute the correlation between two variables.

## Chapters 7 & 8

- Know how to perform a simple linear regression to describe the relationship between a response and an explanatory variable.
- Know that if the explanatory and response variables are switched, the regression line changes, even when plotted on the same axes (unless there is no scatter in the data).
- Know that both correlation and simple linear regression are only appropriate if the form of the association between the variables is linear.
- Know that both correlation and simple linear regression are only appropriate for quantitative variables. (The book does discuss alternatives for ordinal variables, but we didn't cover those in any detail.)
- Know that both correlation and simple linear regression can be sensitive to outliers. Outliers can make the interpretation of results of correlation and regression suspect, and not descriptive of the rest of the data.
- Likewise, know that if a strong association between variables is nonlinear, the correlation coefficient will not reveal the full strength of the association.
- Know that the best way to discern the appropriateness of the linear model (on which both correlation and simple linear regression are based) is by looking at the residuals of the simple linear regression. The linear model is appropriate if the residuals are a horizontal band of points around zero, with no structure. Be able to plot the residuals versus X-values for this purpose.

## Chapter 11

- Know what it means to draw a sample from a population. Be able to explain the meaning of sample and population in this context.
- Know what a statistic is, and give examples.
- Know what a parameter is, and give examples.
- Be able to explain why a voluntary response sample can be biased.
- Be able to explain why a convenience sample can be biased.
- Explain response bias.
- Explain nonresponse bias.
- Explain undercoverage as a source of sampling bias.
- Explain a simple random sample.

## Chapter 12

- Explain what it means for a result to be statistically significant (that the result is strong enough that it is unlikely to occur by chance).

## Chapter 13 & 14 & 15

- Know what a set is, what an element of a set is, and what a subset of a set is.
- Know the symbols for "subset," "element of," "empty set," "intersection," "union," and "complement of."
- Know what it means for two sets to be disjoint.
- Given two sets, find their union and intersection.
- Be able to identify the sample space of a random phenomenon (set of outcomes).
- Be able to list all the events of random phenomenon with two or three outcomes (remember than an event can have 0, 1, 2, or more outcomes).
- Given a sample space and an event find the complement of the event.
- Remember and be able to apply the 5 rules of probability.
- Know the interpretation of independent events, together with Rule 5 which defines them mathematically.
- Know that a random variable assigns, as a function, a number to each outcome of a random phenomenon.
- Be able to give an example of a random variable defined on the set of outcomes of the throw of a four sided die with colors labeling the sides.
- Be able to give an example of a random variable defined on the set of outcomes of ten coin tosses.
- Be able to give an example of a random variable defined on the set of outcomes of three students sampled from our thirty-student class.
- Be able to compute the mean of a discrete random variable.
- Be able to compute the standard deviation of a discrete random variable.

## New Material for final

- This section, including below, is under construction until I figure out what problems will go on final.

## Chapter 15: Random Variables

- Continuous Random Variables (area under curve ...)
- Discrete Random Variables for comparison.

## Chapter 16: Probability Models

- Bernoulli Trials
- Geometric Model
- Binomial Model
- Approximating Binomial Model with Normal Model
- Uniform Model

## Chapter 17: Sampling Distributions Models

- Of Proportions.
- Of Means.
- Central Limit Theorem.