1
Two Sample Hypothesis Tests & Condence Intervals Homework
For every hypothesis test, I want to see the following steps:
Which test should you use?
Check the assumptions.
What are the hypotheses?
What is the test statistic?
What is the p-value?
Do you re
1
Review for Exam 2 KEY
Summer 2013
July 6-9: Saturday to Monday
*Make sure you arrange for a proctor several days in advance.
The exam will cover:
Condence Intervals
Hypothesis Tests Part 1
Hypothesis Tests Part 2
Formula Sheet
You can bring one 8.5 x 11
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Review for Exam 1 KEY
The exam will cover:
Gathering and Describing Data
Probability Parts 1 and 2
Random Variables
Expected Value and Variance
Binomial Distribution
Normal Distribution
Sampling Distribution
Formula Sheet
You can bring one 8.5 x 11 piec
1
Gathering Data Homework
1. Exercises from book: 3.17, 3.39. 3.53, 3.58, 3.74, 3.75
2. A study compared a group of doctors that took aspirin every day and a group of doctors that took a placebo every
day. They found that the subjects in the aspirin group
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Probability Homework Part 1
Section 4.1
*If you don't have dice, you can use a dice roller online such as http:/www.random.org/dice/
Exercises from the book:
1. 4.2,
2. 4.6,
3. 4.7
More Exercises:
4. What is the probability of getting at least one six i
Probability - Part 2 - Homework
Question 1
a) Not always true because there may be a union
b) No, you do not subtract, but rather, add.
c) No, this just implies that they are independent
Question 2
Data
male
male liers
total liers
73%
See cell calculation
Expected Value and Variance Homework
Question 1
-The mean of the P distribution of X is:
*See Cell Calc*
0.1538
Given data
Val of X
Proby
Question 2
The mean grade in the course is:
Given
0
0.8507
1
0.1448
2
0.0045
1
0.04
2
0.2
3
0.4
0
0.05
2.88
4
0.31
Qu
Binomial Distribution Homework
Question 1
a) No, this is false because if you tossed the same coin 20,000
more times is would gradually become closer to a .5 probability in
either direction. Having so few tosses will discredit your theory.
b) Same respons
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Normal Distribution Homework
Part 1: Shape of Normal Distribution
1. 1.109
2. 1.110
3. 1.120
Part 2: Empirical Rule
4. 1.112
5. 1.113
6. 1.122
7. 1.123
Part 3: Standard Normal Distribution
8. 1.126
9. 1.128
10. 1.129
(a) Hint: z has cumulative proportio
Normal Distribution Homework
Question 1
*On PDF file*
Question 2
*On PDF file*
Question 3
*On PDF file*
Women Men
Given
Mean:
14,297
14060
Question 4
Snd.Dev:
6,441
9065
a)
About
12,882 will fit in the 68% of the standard deviation of the mean
68%
About
2
N
n
x
X
=
=
X
X
=
q
( x1
p
p
s
x 1 p 1 + x 2 p2 + + x k p k
X
x i pi
2
2
X ) p2 + + ( x k
X ) p1 + ( x 2
a
X +a = X + a
X
b
bX = b X
X
Y
X +Y = X + Y
X
a
2
X +a
X
2
X
b
2
b X
X
=
= b2
2
X
Y
2
X +Y
=
2
X
+
2
Y
2
X ) pk
n
n
p
X = np
X
p
x
s
p
x
x
SEx
x
1
Sampling Distribution Homework
Sections 3.3, 5.1, and 5.2
Read book pages 202-209. (Skip Example 3.29 and Example 3.30)
Part 1: Samples and Populations
1. 3.83
2. A marketing research rm wishes to determine if the adult men in Laramie, Wyoming, would be
Sampling Distribution Homework
Question 1
a)
The Population is college students and the sample is 17,096. This is a fact
of the sample. Another way of putting it would me that "ABOUT" 19.4% of
college students are binge drinkers - This assuming that the s
x z p
n
n
30
s
x t p
n
n
1
n
p z
r
30
p
p (1 p)
n
np
10
n (1
p)
10
n=
z
m
n=
2
z
2m
2
n
n
H0 : = 0
z=
x
p0
/n
2
x
s
s
30
n
H0 : = 0
t=
x 0
p
s/ n
df = n
1
p
p
2
30
np0
10
n (1
H 0 : p = p0
z=r
p
p0
p0 (1 p0 )
n
p0 )
10
114
x = 3077
n = 114.
s = 987
s
x t
1
Probability Homework Part 1 KEY
Section 4.1
*If you don't have dice, you can use a dice roller online such as http:/www.random.org/dice/
Exercises from the book:
1. 4.2,
2. 4.6,
3. 4.7
4.2. The overall rate (56%) is an average. Graduation rates vary gr
From the article on moms having few interactions with their infants during tv time, there
are a lot similarity between the online article and the book. Infant and mother interaction is not
something that needs to be taken lightly. Mother infant relationsh
From the article on moms having few interactions with their infants during tv time, there
are a lot similarity between the online article and the book. Infant and mother interaction is not
something that needs to be taken lightly. Mother infant relationsh
Figure 1
It appears in 2007, most individuals had a higher rate between 3.5 and 4.0
of an incident rate of cryptosporidiosis (CDC, 2017). In 2008, the second to highest
rate being between 3.0 and 3.5 appears to be the time most affected by the higher
inci
Martin Luther King Juniors speech, The Mountain Top, is his last speech before his
assassination the following day. Throughout Kings Mountain Tops speech, we learn that he has
reached a point to where anyone who is against them, and anyone that is fightin
4. Public health official Dr. Tony Iton says of immigrant health, Theyre
doing something right. What conditions in the Bernals lives protect or
promote their health? What do these conditions protect them from? What
might cause their health to decline over
27
28. All the books published by a certain publisher have a mean of 256 pages and a standard deviation of 23 pages.
A random sample of books by the publisher have a mean of 243 pages and a standard deviation of 19 pages.
(a) Summarize the given informati
x z p
n
n
30
s
x t p
n
n
1
n
p z
r
30
p
p (1 p)
n
n
p
10
n (1
p)
10
n=
z
m
n=
2
z
2m
2
n
n
H0 : = 0
z=
x
p0
/ n
2
x
s
s
30
n
H0 : = 0
t=
x 0
p
s/ n
df = n
1
p
p
2
30
np0
10
n (1
H 0 : p = p0
z=r
p
p0
p0 (1 p0 )
n
p0 )
10
2
We use a chi-square test statistic
(observed counts-expected counts)
2
X2 =
expected counts
all cells
with k 1 degrees of freedom.
k
is the number of groups/categories
*If our observed counts and expected counts are really dierent, what kind of numbers
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Condence Intervals Homework KEY
Condence Interval for Population Mean ( is known)
x z
n
Assumption: normal population or
n 30
Condence Interval for Population Mean ( is unknown)
s
x t
n
Degrees of freedom:
n1
Assumption: normal population or
n 30
Cond
x=
x1 + x2 + x3 + + xn
n
s2 =
P (A
( x1
2
x) + ( x2
2
x) + + ( xn
n1
) = P ( A) + P ( B )
P (A | B ) =
P(
P(
)
P (B )
P(
) = P (A | B ) P (B )
P(
) = P ( A) P ( B )
x)
2
)
X = x 1 p 1 + x 2 p2 + + x k p k
q
2
2
( x 1 X ) p 1 + ( x 2 X ) p2 + + ( x k
X=
2
x z p
n
n
30
s
x t p
n
n
1
n
p z
r
30
p
p (1 p)
n
np
10
n (1
p)
10
n=
z
m
n=
2
z
2m
2
F
F
T
x
P (22 < < 28) = 0.99
x
= 10
x = 150
C
C
n
x
= 0.01
n
n = 100
n = 196
n = 10000
n = 38416
D
x = 66.2
= 4.1
C
A
= $30
C
= 2.5
x = 29.6
B
A
Yes
We don't know.
No
Y