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STP420, Review notes for Test #2 Summer 2002.
1. Know new vocabulary and symbolic notation :
 random variable (discrete, continuous)
 probability distribution of random variable
 Law of large numbers
 normal and standard normal distribution curves
 standardized version of normal variable, z-score
 t distribution, degrees of freedom
 Sampling errors
 Sampling distribution of counts, proportions and , Central Limit Theorem
 Binomial distribution, normal approximation
 Confidence interval, confidence level (C), margin of error (m)
 Standard error of a statistics.
 Null and alternative hypotheses
 Two - sided, left-sided, right-sided alternative hypothesis
 test statistics, significance level of the test (), p-value
 Pooled sample standard deviation, pooled sample proportion
 Matched (paired) samples
2. Probability
11.Know simple probability rules: 0  P(A)  1
P(Ac)=1-P(A)
P(AorB)= P(A)+P(B)-P(AandB)
For disjoint events
P(AorB)= P(A)+P(B)
For independent events
P(AandB)=P(A)*P(B)
11. Know what is the sample space, event, what are events: Ac, AorB, AandB
List sample spaces for simple experiments, like:
Roll die once, Roll die 2 times, Select a card from an ordinary deck,
Toss two coins, Toss 3 coins
Know when events are mutually exclusive (disjoint) or independent.
How to illustrate events using Venn diagrams.
Compute probabilities from 1- way and 2-way frequency tables.
Compute probability based on independence.
2.
Know what is the random variable, discrete and continuous.
Know how to obtain the probability distribution for a random variable and how
to compute different probabilities associated with the discrete and continuous
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random variables.
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Know the rules for means and variances of random variables
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Be able to compute mean and standard deviation for discrete and
continuous random variable.
3.
 Know the properties of normal ,standard normal and t curves (Center at ,
symmetry, area=1)
 Know how to find areas under standard normal and normal curves using tables,
use symmetry.
 Remember how to compute mean and standard deviation for a sample and for a
population.
 Know how to compute mean and st. deviation of a random variable.
 Know rules for means and standard deviations of random variables.
(Chapter 4, 4.4)
4. Remember our assumptions for CI and Hypothesis tests:
1. Normal populations or large samples.
2. Independent samples for tests for two population means and proportions.
(Tests and CI for proportions, Ch8,will be included on the final)
3. If samples are matched, differences should be normal or large samples.
4. Large populations, much larger than a sample, for proportion inferences (np
 10, n(1-p)  10)
4. All samples are SRS.
5. If we have a small samples and no normality assumption, use nonparametric
methods (There are some described in the book, we did not talk about them and
it won’t be included on test)
5.
 Know the sampling distribution of sample counts and sample proportion. How
and when to use a normal approximation.
 Binomial distribution for counts, use binomial tables or binomial formula.
 Know what is the sampling distribution of the sample mean ( ), know mean and
standard deviation of (  =  and  =/n).
 Know how the shape of the distribution changes with increasing sample size n.
 Know when has normal distribution, when approximately normal distribution.
Know Central Limit Theorem.
 What is the standard version of .
 Use the standard version of to answer questions like:
What is P( > 14), where is a sample mean of a sample of size 6 from normally
distributed population with mean of 10 and std. deviation of 5.
6.
 Know that is a point estimate of .
 Know how to compute Confidence Interval for  with C confidence level
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1. when  is known (Z-interval)
2. when  is unknown (t-interval)
Know why t interval is wider than z interval for given C and n.
Interpret the CI
What is the margin of error (m) for a given CI, know how it changes with
increased sample size and the same confidence level.
Estimate the sample size for given m and confidence level.
What is the standard error of the .
7.
 Know all the steps in testing the hypotheses
How to select appropriate Ha
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 Know how to compute a p-value for an observed test statistics for different Ha.
 When you reject Ho, for given significance level :
(when (P-value < ) , reject Ho otherwise fail to reject Ho
 Know that when null hypothesis is rejected, you have evidence for alternative,
but when you fail to reject null, there is no evidence for alternative ( for given
significance level )
 Know that you use z-test when  is known and
t-test when  is unknown.
 Know how one sample two-sided Z-test and t-test for  are connected with zinterval and t-interval procedures.
8.
 Know the sampling distribution of 1- 2 for independent samples.
 Know how to test Ho: 1=2 versus appropriate alternative hypothesis in each of
the cases (for independent samples):
1.Known population standard deviations (2 samples z-test)
2.Unknown population standard deviations (but assumed equal)
(2 samples t- test, pooled standard deviation)
3. Unknown population standard deviations ( not assumed equal)
(2 samples approximate t- test, use df= Smaller sample size - 1 or
use calculator estimated df. )
 Know how to test Ho: 1=2 versus appropriate alternative hypothesis for
matched samples (t- test for )
 for all the cases above know how to compute and interpret CI for
1-2.
 Know connection between two-sided hypothesis test and confidence interval for
1-2.
9. Chapter 8-this will be covered on the final.
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Hypothesis test and confidence interval for one population proportion, and
selecting a sample size for estimating p.
Know the sampling distribution of p1-p2 for large independent samples.
Know how to test Ho: p1=p2 versus appropriate alternative
Know how to compute and interpret CI for
p1-p2
Know connection between two-sided hypothesis test and confidence interval for
p1-p2
10.
Chapter 9-this will be covered on the final.
10. Know how to interpret information from 2 and 3-way contingency tables. Know
how to obtain marginal and conditional distributions. Be able to identify all types of
association between the variables (Common response, Causation, Confounding). Be
able to explain and give an example of Simpson’s Paradox. Be aware what are the
lurking variables.
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Know properties of Chi-square distribution curve and be able to use Chisquare table.
Be able to perform Goodness-of-fit test (examples done in class)
Be able to perform Test of independence (no association)
Check following problems in addition to examples done in class:
9.1, 9.6, 9.9, 9.12, 9.18, 9.21, 9.23