Statement on the Grading of Exams On the exams, I am testing your ability to actually correctly solve the problems. The point of statistics is to arrive at the correct final answer. For example, if you are working as a research assistant and you are asked
Completing Blackboard Problem Sets The Blackboard problem sets will be posted under Assignments. Click on the problem set and it will open up. You should then print out the problem set. You can exit Blackboard. Solve the problems and write down the answer
6.2
Tests of Significance
Example #1 borrowers at private 4-year college: mean debt ( a )= $21,200 (survey result) borrowers at public 4-year college: mean debt ( b )= $17,100 (survey result) the difference $4100 ( a - b ) is fairly large/ but these numbe
4.4
Means and Variances of Random Variables Mean of a discrete random variable
Suppose that X is a discrete random variable whose distribution is Value of X Probability x1 x2 x3 xk p1 p2 p3 pk
To find the mean of X, multiply each possible value by its pro
4.2
Probability Models
probability model- a description of a random phenomenon in the language of mathematics the description of a random variable has two components: a list of possible outcomes a probability for each outcome The sample space S of a rando
4.1
Randomness
toss a coin- cant predict result in advance (results vary) a regular pattern emerges after many repetitions We call a phenomenon random if individual outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a la
3.3 Toward Statistical Inference Statistical inference is using a fact about a sample to estimate the truth about the whole population. A simple random sample (SRS) of size n consists of n individuals from the population chosen in such a way that every se
3.2 Sampling Design population- the entire group of individuals we want information about sample- the part of the population that we actually examine in order to gather information sample survey- survey a sample to gain info about the population voluntary
3.1
Design of Experiments
experimental units- individuals on which the experiment is done subjects- experimental subjects that are humans treatment- specific experimental condition applied to the units factors- explanatory variables in experiment levels-
2.6 The Question of Causation Often the goal in a study is to establish that changes in the explanatory variable cause changes in the response variable. What constitutes good evidence of causation? What different types of links between x and y can explain
2.4
Cautions about Correlation and Regression
regression- after fit a line to data, can see scatter of data points about regression line regression makes sum of squares of vertical distances from the data points and the regression line are as small as pos
2.3
Least-Squares Regression (OLS)
correlation measures the direction and strength of the linear relationship between two quantitative variables we would like to summarize the overall pattern by drawing a line on the scatterplot A regression line is a str
2.2
Correlation
scatterplots display the relationship between two variables linear (straight-line) relationships are important because they are quite common linear relationship is strong if points lie close to a straight line linear relationship is weak i
Chapter 2- Looking at Data we often care about the relationship between two variables to study the relationship, we measure both variables on the same individuals Two variables measured on the same individuals are associated if some values of one variable
Normal Quantile Plots Normal quantile plots are used to determine whether or not data distributions are normal. Constructing a normal quantile plot 1. Arrange the observed data values from smallest to largest. Record what percentile of the data each value
1.3 Density Curves and Normal Distributions
Density Curve idealized description of data distribution smooth approximation to the irregular bars of a histogram Density Curve The curve is always on or above the horizontal axis. The curve has area exactly 1
9.1 Inference for Two-Way Tables exclusive territory- new store will be the only representative of the franchise in a specified territory and will not have to compete with other outlets of the same chain Effect of having an exclusive territory on the succ
8.1 recall from 5.1, when n is large:
Inference for a Single Proportion p ~ N (p, p (1 p ) ) n
Large-sample confidence interval for a population proportion Choose an SRS of size n from a large population with unknown proportion p of successes. The sample
7.2
Comparing Two Means
two-sample problems are among the most commonly encountered in statistics compare control group and treatment group Two-sample problems the goal of inference is to compare the responses in two groups each group is considered to be
7.1
Inference for the Mean of a Population
the sampling distribution of x depends on when is unknown, we must estimate even though we are primarily interested in the sample standard deviation (s) is used to estimate the population standard deviation ()
)
6.2
Tests of Significance
Example #1 borrowers at private 4-year college: mean debt ( a )= $21,200 (survey result) borrowers at public 4-year college: mean debt ( b )= $17,100 (survey result) the difference $4100 ( a - b ) is fairly large/ but these numbe
6.1
Estimating with Confidence
those who took the SAT math in 2003: mean= 519, sd= 115 give test to SRS of 500 California students: x = 461 (math) What can you say about the mean score in population of 385,000? x is an unbiased estimator of ( x = ) but ho
5.2
The Sampling Distribution of a Sample Mean
Figure 5.8 averages are less variable than individual observations averages are more normal than individual observations
The mean and standard deviation of x
2 x = mean of sample, = mean of population
, 2 = p
5.1
Sampling Distributions for Counts and Proportions
link between Chapter 4 (probability theory) and rest of book
Statistical inference draws conclusions about a population or process on the basis of data. The data are summarized by statistics such as me
4.5
General Probability Rules Previous Probability Rules
1) The probability P(A) of any event A satisfies 0 P(A) 1. 2) All possible outcomes together must have probability 1. P(S) = 1. 3) Two events A and B are disjoint 4) The complement rule states that
4.4
Means and Variances of Random Variables Mean of a discrete random variable
Suppose that X is a discrete random variable whose distribution is Value of X Probability x1 x2 x3 xk p1 p2 p3 pk
To find the mean of X, multiply each possible value by its pro
4.3
Random Variables
random variable- a variable whose value is a numerical outcome of a random phenomenon toss coin 4 times could record outcome as string of heads and tails (HTTH) let X be number of heads X=2 (X is random variable) Discrete random varia
4.2
Probability Models
probability model- a description of a random phenomenon in the language of mathematics the description of a random variable has two components: a list of possible outcomes a probability for each outcome The sample space S of a rando
4.1
Randomness
toss a coin- cant predict result in advance (results vary) a regular pattern emerges after many repetitions We call a phenomenon random if individual outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a la
3.3 Toward Statistical Inference Statistical inference is using a fact about a sample to estimate the truth about the whole population. A simple random sample (SRS) of size n consists of n individuals from the population chosen in such a way that every se