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
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
1
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
Condence IntervalsIntroduction
Point Estimates
We can use the sample mean x as an estimate of the population mean .
(We call it a point estimate because the sample mean is just one number, or a single point.)
Example 1. We want to estimate the true popula
1
Condence Intervals Homework
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
Condence
Condence IntervalsIntroduction
Point Estimates
We can use the sample mean x as an estimate of the population mean .
(We call it a point estimate because the sample mean is just one number, or a single point.)
Example 1. We want to estimate the true popula
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
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
1
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
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
1
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
1
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
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
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
Confidence Intervals Homework
Question 1
a)
Between 77 and 97
b)
If you want to be confident that you have included the correct
mean in your sample size you have to have are larger margin of
error.
Question 2
*See PDF*
Question 3
* See PDF*
Question 4
a)
1
Basic Hypothesis Tests Part 2
Section 7.1 One Sample T Test for Mean
1. 7.20
2. 7.21
3. 7.22
4. 7.25
5. 7.28ab
6. 7.33a
Section 8.1 One Sample Proportion Z Test
7. 8.26b
8. 8.31
9. 8.32
10. 8.39a
General Questions for Hypothesis Tests
11. In the last ma