1. A poker-dealing machine is supposed to deal cards at random, as if from an infinite deck.
In a test, you counted 1600 cards, and observed the following:
Spades
Hearts
Diamonds
Clubs
404
420
400
376
Could it be that the suits are equally likely? Or are these discrepancies too much to be random?
2. Below is a copy of world population estimates during given years. Develop a best fit mathematical model for
these data.
Year
(millions)
Pop
Chart Title
y = 75.255x - 144462
R² = 0.9945
8000
1000
1750
1800
1850
1900
1950
1955
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
2010
310
791
978
1262
1650
2519
2756
2982
3335
3692
4068
4435
4831
5263
5674
6070
6454
6972
7000
6000
5000
4000
3000
2000
1000
0
1940
1950
1960
1970
1980
1990
2000
2010
ANOVA
df
Regression
Residual
Total
SS
MS
F
1 25768046 25768046 1974.3519
11 143565.3 13051.39
12 25911611
Significance F
9.16138E-14
2020
3. Evaluating Textbooks
Does the new math program improve student performance?
Suppose you take a random sample of 20 students who are using a new algebra text which features group work
and unit summaries and a second sample of 30 students who are using a more traditional text. You compare
student achievement on the state test given to all students at the end of the course. Use the frequency table to
determine if the proportions from each group are equal at each performance level.
Below grade level
At grade level
Advanced
New text
8
6
6
Old text
6
15
9
Test Outline
Bring a calculator and one sheet of paper with anything you want on it.
1. What is the exact probability that between 5 and 8 students (inclusive) out of 10 pass a statistics
final exam if the probability of passing the exam is .65? Show work.
Hint: P(X = K successes) = C(n,k)*p^k*(1-p)^(n-k) where p is the probability of a single
success in a Bernoulli trial.
2. Suppose the survival rate of Ebola Virus Disease patients in the US is 71.5%. Determine the
probability that 1800 US Ebola Patients in a sample of 2000 will survive. Is this number
significantly different from what is expected? Use your calculator.
3. Scenario: Solve the above problem by hand using proportions.
4. Scenario: Chi-square Test of association
5. Scenario: Chi-square Test for independence
6. Scenario: z-test
7. Scenario: t-test
8. Scenario: two sample t-test
9. Scenario: paired sample t-test (really a t-test of differences between paired scores.)
10. Scenario: two sample t-test vs two sample t-test; which is better?
11. Linear regression
a.
b.
c.
d.
e.
Find the best fit model
Test the model for significance
Interpolate and Extrapolate with the model
Know the three types of error in a linear model and how to define them
Interpret the calculations on a generic ANOVA regression table.