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BST 611 (Beasley) Homework 2 (100 points)
Use the following Sample Data for Questions 1 – 5.
Male
Female
Honda
60
70
Toyota
58
46
Nissan
84
56
Mazda
46
26
Mitsubishi
32
24
1. What is the Marginal Probability of randomly selecting a female from this sample of car owners?
P(F) =
(2 points)
2. What is the Marginal Probability of randomly selecting a Honda owner from this sample of car
owners? P(Honda) =
(2 points)
3. What is the Conditional Probability of randomly selecting a Nissan owner given that she is female
from this sample of car buyers?
P(Nissan | F) =
(2 points)
4. What is the Joint (Intersection) Probability of randomly selecting a Male Mazda owner from this
sample of car buyers?
P(M ∩ Mazda) =
(2 points)
5. What is the Joint (Union) Probability of randomly selecting a Male or a Mitsubishi owner from this
sample of car buyers?
P(M U Mitsubishi) =
(2 points)
6. Suppose flipping an unbiased coin four times. List all possible outcomes (show the sample space).
(5 points)
7. What’s the Joint Probability of flipping 4 consecutive Heads? P(H = 4) =
(2 points)
8. What is the frequency distribution for the Sum of Number of Heads?
(4 points)
Number of Heads
0 Heads
1 Head
2 Heads
3 Heads
4 Heads
Frequency
9. What is the Probability of flipping 3 or more Heads in 4 flips? P(H ≥ 3) =
(4 points)
1
BST 611 (Beasley) Homework 2 (100 points)
10. Suppose rolling a single (N=1) unbiased six-sided die. Calculate the Mean, Variance, and Standard
Deviation from the following frequency distribution. 4. You can do this by hand or use either SPSS
(Analyze-Descriptive Statistics-Explore); JMP (Analyze-Distribution); or
SAS (PROC UNIVARIATE; PROC BOXPLOT).
(4 points)
Roll
1
2
3
4
5
6
Freqeuncy
1
1
1
1
1
1
Y =
sY2 =
sY =
11. Take the data in BST611Assn2-2rolls.xls and Import it into SPSS, JMP, or SAS. 4. Use either
SPSS (Analyze-Descriptive Statistics-Explore); JMP (Analyze-Distribution); or SAS (PROC
UNIVARIATE; PROC BOXPLOT) to report the following statistics.
(12 points)
Roll 1
Roll 2
Sum
Mean
Y1 =
Y2 =
YSUM
=
YY =
s12 =
s22 =
2
sSUM
=
sY2 =
s1 =
s2 =
sSUM
=
sY =
12. Using the concept of the Central Limit Theorem, describe how the Means, Variances, and Standard
Deviations in Question 11 relate the Mean, Variance, and Standard Deviation in Question 10.
(5 points)
13. Using the concept of the Central Limit Theorem, discuss the shape of the distribution of the Mean
of Rolls as compared to the shape of the distribution of a Single Roll.
(5 points)
14. Use either SPSS (Analyze-Correlate-Bivariate); JMP (Analyze-Multivariate MethodsMultivariate); or SAS (PROC CORR) to compute the Pearson correlation between Rolls 1 and 2.
(2 points)
Pearson r12 = ___________
15. What does this correlation (r12) imply?
(2 points)
16. Using the concept of the Central Limit Theorem, discuss the Mean, Variance, Standard Deviation,
and the shape of the distribution of the Mean of Rolls for rolling N = 16 dice simultaneously.
(5 points)
17. If you were to roll N = 16 dice simultaneously, what is the Probability that the Mean Roll would be
equal to or exceed 5.375 (sum of 86 or greater); P( Y ≥ 5.375) =
(4 points)
2
BST 611 (Beasley) Homework 2 (100 points)
18. Suppose the Distribution of GRE-Quantitative (Q) scores is Normal with a  = 500 with  = 100.
18.1. What is probability of randomly selecting a person with a score greater than or equal to 625?
P(Q ≥ 625) =
(4 points)
18.2. What is probability of randomly selecting N=10 people with a Mean score greater than or
equal to 525?
P( Q ≥ 525) =
(4 points)
19. Frattola et al. (2000, Hypertension, 36, 622-628) found the Standard Deviation of 24-hour Diastolic
Blood Pressure (DSP) among Diabetics to be 12. The average 24-hour DSP was 76. Assume these
values are representative of the population parameters (Y = 76; Y = 12) and the shape the DSP
distribution is Normal. Now suppose N = 6 patients were given Lacidipine. What is the probability that
these patients will have a mean DSP of 70 or less? P( Y ≤ 70 | [Y = 76; Y = 12]) =
(7 points)
20. Suppose a similar situation with the DSP among Diabetics being Normally Distributed with a
Standard Deviation of 24-hour DSP among Diabetics to be 12 (Y = 12). Suppose researchers
randomly assigned nC = 4 patients to a control condition given a placebo and nT = 6 patients to a
treatment condition given Lacidipine. The results showed that the Control group had a Mean DSP of
YC = 75 and the Treatment group had a Mean DSP of YT = 71. The assumption is that population
means for these groups are expected to be equal if there is No Treatment effect for Lacidipine. If the
population means are equal this implies that the difference in population means will be zero
[(T - C) = D = 0]. What is the probability that a Mean Difference this extreme or larger occurred by
chance assuming No Treatment effects? P( YD ≥ 4 | [D = 0; Y = 12]) =
(7 points)
21. Suppose a coin was flipped 40 times, assuming an unbiased coin, what is the probability of get 30
or more Heads? P(H ≥ 30 | [p = .50]) =
(7 points)
22. Suppose a researcher was interested in a smoking cessation treatment. Suppose the researcher
randomly assigned nC = 8 patients to a control condition given a placebo and nT = 10 patients to a
treatment condition given nicotine patches. The assumption is that population proportions of quitting
for these groups are expected to be equal if there is No Treatment effect for the nicotine patches. After
4 weeks, the results showed that the Control group had 2 people quit and the Treatment group had 6
people quit. What is the probability that a Proportional Difference this extreme or larger occurred by
chance assuming No Treatment effects? P( p̂D ≥ x? | [pD = 0]) =
(7 points)
3