In class part of final: Wednesday, August 18, 2010.
Takehome part of final: Opens Monday, August 16, at 9:00pm,
due on Saturday, August 21 at noon.
Read in TextBook
Chapters 4, 5, 6, 7, 8.
Format of Exam Questions
Short answer, multiple choice, short essay, problems,
SPSS analysis
Persons
Know these persons:
Jacob Bernoulli first proved the LLN in 1713.
Abraham de Moivre first stated the Central Limit Theorem (CLT) in 1733.
Alexandr Lyapunov first proved the CLT in its modern form in 1901.
Definitions
Controlled, double blind, randomized experiment, observational
study, confounding factors (also called lurking variables),
histogram, density histogram, bin, mean,
median, standard deviation, variance, Q0, Q1, Q2, Q3, Q4, IQR,
boxplot, normal plot, mild outliers, extreme outliers, normal histogram,
ideal measurement model,
center, spread, standard normal curve, critical points, inflection points,
standard units, standard error of the mean, normal score (Van der Waerden's
method), normal plot, probability, ways to obtain probabilities
(theoretical, frequentist,
subjective), fair bet, mutually exclusive events, the addition rule,
independent events, the multiplication rule, n factorial (n!),
0! = 1, binomial formula, random variable (rv), probability
distribution, expected value of a rv, theoretical SD of a rv,
sample mean and SD,
expected value and SE for average in ideal measurement model,
expected value and SD for Bernoulli random
variables, law of averages (law of large numbers = LLN),
central limit theorem = CLT, normal approximation,
confidence interval for p, confidence interval for μ,
the 5 steps to a test of hypothesis,
null hypothesis, alternative hypothesis, test statistic, z-test for average,
z-test for percentage, t-test, confidence intervals for z-tests and for
t-tests, p-value, paired sample z- and t-tests,
importance vs. significance, data snooping, one-tailed tests.
Know both the defining formula and the intuitive idea behind the
concept.
Know How To
Find x, and SDx,
compute the z-score.
Use the normal table to determine the proportion of observations in
a bin of the form [a, b], (-∞, a], or [a, ∞).
Interpret a normal plot. Usual descriptions are fairly normal,
skewed to the left, skewed to the right, fat tails, thin tails.
Calculate probabilities using the addition rule, the multiplication rule,
the binomial formula.
Use the formula 1 - (1 - p)n to calculate
probability of at least one success out of n Bernoulli trials.
Compute the expected value and SE for the sum of random variables.
Compute confidence intervals for the sum of Bernoulli random variables.
Compute the confidence interval for μ in the ideal measurement
model.
Perform the 5 steps of a test of hypothesis, either by hand or
using SPSS output:
Write down the null and alternative hypotheses.
Compute the test statistic,
assuming that the null hypothesis is true.
Write down a 95% confidence interval. ( (-1.96, 1.96) for a
z-test. Use standard normal table to get confidence intervals of other
sizes.
Decide whether to accept or reject the null hypothesis.
Compute the p-value. Accept the null hypothesis if p > 0.05 and
reject the null hypothesis if p < 0.05.
Compute confidence intervals using the normal table and using the
t-table. Look at the bottom of the t-table to get confidence intervals
easily.
Perform these tests of hypothesis by hand: one sample z-test for μ,
one sample z-test for S, paired-sample z-test.
Perform these tests by hand and/or using SPSS output: one sample t-test,
paired-sample t-test.
Interpret a boxplot.
Interpret a normal plot.
Explain
Be able to explain in terms that someone not very familiar with
statistics will understand:
How are probabilities determined?
What is the Law of Averages and how is it commonly
misstated?
Why is the CLT so important in statistics?
What does it mean for a result to be statistically significant?
Why is statistical significance not the same as importance?
Explain what a test of hypothesis is and some things to watch out for
when using a test of hypothesis.