+
1
Student example 6
L2, p.15
State has 5 unis, 25 TAFE, 5 private colleges
Satisfaction Survey of 700 business students in State
how to best representatively sample this population?
+
STA1010 Statistical
Methods for Science
Lecture 3
Looking at Data: H
+ Means of Random variables (L16,P106)
1
Mean also know as EXPECTED VALUE, E(X)
Know probability distribution mean can be determined:
The mean of a discrete random variable X is:
n
x E ( X ) xi . p i .
i 1
summed over all possible outcomes
+ Example 2:
2
+
STA1010 Statistical
Methods for Science
Lecture 13:
The law of total probability
+
2
Summary of Lecture 12
Definition of probability
Law of large numbers
What is a sample space?
Probability Rules
+
3
Probability Rules
+
4
Outline of Lecture 13
The Law o
+
1
Correlation , r
L8, pp. 5456
= measure of direction and strength
of the linear relationship
Better fit = closer fit = smaller residuals overall
(assuming linear IS OK)
both variables must be quantitative
no distinction between explanatory and respo
+ Linear Transformations
1
(L5, p 3132)
Consider the values: 5, 11, 3, 15, 8.
Five number summary is (3,5,8,11,15)
IQR is 6
Mean is 8.4
SD is 4.77
Add 10 to every data point. What happens to:
Five number summary
IQR
Mean
SD
+ Linear Transformations
2
(L5
+ General formula for Binomial
(L14,p98)
Binomial probability mass function
for each discrete outcome:
where r = 0, 1, 2, 3, , n
written as X ~ B(n, p)
1
+
2
Student Example 9
(L14,p99)
How many ways can you select 3 of the
numbers
1, 2,., 10?
How many wa
+
1
Testing for disease
Example 3. Digitalis intoxication (L6, page 37)
Contingency Table between:
Disease presence: D+ (have disease) and D (do NOT have disease)
and
Diagnostic Test result: T+ (test is positive) and T  (test is negative)
Note
D+ and T
+
STA1010 Statistical
Methods for Science
Lecture 12:
Probability of Events
+
2
Shortlisting
An actuarial firm hires candidates by setting two problems.
Those who correctly answer one of the problems get shortlisted
for an interview. Past experience shows
+
STA1010 Statistical
Methods for Science
Lecture 18
Calculations with Normal Random Variables
+
2
Summary of Lecture 17
The Normal Distributions
Continuous random variables
Density curves
Normal distributions
Q: What is this?
Standardising observations
T
+
STA1010 Statistical
Methods for Science
Lecture 19
Testing for Normality
+
2
Summary of Lecture 18
The probability that a random variable
takes a value in some range is the area
under the pdf in that range.
Can standardise normal RVs to produce
an RV wi
DEPARTMENT OF MATHEMATICS
TRENT UNIVERSITY
MATH 1052H: NonCalculus Statistics II (Elementary Statistics Methods)
2017 Summer
Peterborough
Distance Education/Online
Instructor: Dr. Haile Gessesse
Trent Email: hailegessesse@trentu.ca
Telephone:
(705) 7481
Last Name: _
First Name: _
ID: _
MATH1051  NonCalculus Statistics I  Elementary Probability and Statistics
Lab 3
Inferences from One Samples
Objectives:
1. Use Rcmdr to construct a twosided confidence interval of a
population mean and variance.
2. Use
Last Name: _
First Name: _
ID: _
MATH1052  NonCalculus Statistics II  Elementary Statistical Methods
Lab 2
Multiple Linear Regression Models
Objectives:
Use Rcmdr to fit a multiple linear regression model, construct ANOVA tables,
test of usefulness of
Calculus I: Functions and calculus of one variable
MATH 1101

Spring 2012
Waive WMIM!
W Th; Wm Theme:
5) v MN: chugG
f '60 1. F(x+h) 40:) w."er/"b " VJw . 3" 3 f h) mumu)
_ l" I :
n ho h 4'; 0;nv b a! 51:41
Datum Rule: "7rwde b ' '
_._ .3 Nona) power. on. Smoogq): 5.
7 Coaltold):
Question 1
(7 Determine whether the given value is a statistic or a parameter.
k
A sample of 120 employees of a company is selected, and the average age is found to be 3? years.
Selected Answer 0 Statistic
Answers: Parameter
o Statistic
Question 2
(7a D
Find the indicated probability.
The probability that an event will occur is 0.3. What is the probability that the event will not occur?
Selected Answer:
0.7
Answers:
0
0.7
0.3.
Response Feedback: 10.3
Question 2
1 out of 1 points
Let A and B be two even
Express the confidence interval using the indicated format.
Express the confidence interval 0.38 < p < 0.54 in the form of
E.
Selected Answer:
0.46 0.08
Answers:
0.46 0.16
0.38 0.16
0.46 0.08
0.38 0.08
Response Feedback: phat =(0.54+0.38)/2; E = (0.540
Which of the following describes a probability distribution?
Selected Answer:
Answers:
x
P(x)
1
0.2
3
0.5
6
0.3
x
P(x)
7
0.12
10
0.29
16
0.15
x
P(x)
1
0.2
3
0.5
6
0.3
x
P(x)
0
0.2
5
0.6
8
0.3
22
0.01
None of the above.
Question 2
1 out of 1 points
Find t
1.
QUESTION 1
Answer the question, considering an event to be "unusual" if
its probability is less than or equal to 0.05.
Is it "unusual" to get 11 when a pair of dice is rolled? (correct answer is no)
Ye
s
No
1 points
QUESTION 2
1.
Answer the question.
W
Find the indicated critical z value.
Find the value of z/2 that corresponds to a confidence level of 89.48%.
Selected Answer:
1.62
Answers:
0.0526
1.62
1.62
1.25
Response Feedback: = 10.8948
Question 2
1 out of 1 points
Solve the problem.
The following
For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the
normal distribution as an approximation.
n = 62 and p = 0.7
Selected Answer:
Normal approximation is suitable.
Answers:
Normal approximation i
Determine whether the given value is a statistic or a parameter.
After taking the first exam, 15 of the students dropped the class of 68 students. Assume the population is the class
of the 68 students. The proportion 15/68 is a ?
Selected Answer:
Paramet
Question 1
1 out of 1 points
Assume that X has a normal distribution, and find the indicated probability.
The mean is = 15.2 and the standard deviation is = 0.9.
Find the probability that X is greater than 15.2.
Response
Feedback:
P(x>15.2) = P(z>(15.215.
MATH1051  NonCalculus Statistics I  Elementary Probability and Statistics
Lab 3
Inferences from One Samples
Objectives:
1. Use Rcmdr to construct a twosided confidence interval of a population mean and variance.
2. Use Rcmdr to conduct hypothesis test
Last Name: _
First Name: _
ID: _
MATH1051  NonCalculus Statistics I  Elementary Probability and Statistics
Lab 3
Inferences from One Samples
Objectives:
1. Use Rcmdr to construct a twosided confidence interval of a population mean and variance.
2. Use
Last Name: _
First Name: _
ID: _
MATH1051  NonCalculus Statistics I  Elementary Probability and Statistics
Lab 3
Inferences from One Samples
Objectives:
1. Use Rcmdr to construct a twosided confidence interval of a
population mean and variance.
2. Use
Age
18
20
43
39
60
18
57
27
20
18
63
20
24
46
29
63
21
45
40
50
48
64
18
50
20
20
47
19
55
23
21
19
64
30
43
23
64
40
23
44
60
24
49
62
53
18
41
21
21
Gender
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
F
F
F
F
F
F
F
F
F
Last Name: _
First Name: _
ID: _
MATH1051  NonCalculus Statistics I  Elementary Probability and Statistics
Lab 4
Inferences from Two Independent Samples
Objectives:
1. Use Rcmdr to conduct hypothesis tests of equality of variances of two
independent po