Test of a hypothesis
A sewer pipe manufacturer claim that, on average their
pipes have breaking strength beyond 2,400 pounds.
Suppose you have a dataset consisting 50 measurements,
namely the breaking strength measured on 50 sections of
a sewer pipe the c
LECTURE VI
STAT 515
February 2, 2010
University of South Carolina
Lecture 6 p.1
Mean and standard deviation
Let X Uniform(c,d), then the probability density
function is given by
1
f ( x) =
dc
for c x d.
It can be computed that
c+d
:= E [X ] =
2
P (a < X
Comparing two population means
Problem: A study published in the Journal
of American Academy of Business, examined whether the perception of the quality of service at ve-star hotels in Jamaica
diered by gender. Hotel guests were randomly selected from th
STAT 515 - Chapter 13: Categorical Data
Recall we have studied binomial data, in which each
trial falls into one of 2 categories (success/failure).
Many studies allow for more than 2 categories.
Example 1: Voters are asked which of 6 candidates
they prefe
STAT 515 - Chapter 11: Regression
Mostly we have studied the behavior of a single
random variable.
Often, however, we gather data on two random
variables.
We wish to determine: Is there a relationship between
the two r.v.s?
Can we use the values of on
STAT 515 - Chapter 10: Analysis of Variance
Designed Experiment A study in which the researcher
controls the levels of one or more variables to determine
their effect on the variable of interest (called the
response variable or dependent variable).
Respon
STAT 515 - Chapter 9: Two-Sample Problems
Paired Differences (Section 9.3)
Examples of Paired Differences studies:
Similar subjects are paired off and one of two
treatments is given to each subject in the pair.
or
We could have two observations on the s
STAT 515 - Chapter 8: Hypothesis Tests
CIs are possibly the most useful forms of inference
because they give a range of reasonable values for a
parameter.
But sometimes we want to know whether one
particular value for a parameter is reasonable.
In this
STAT 515 - Chapter 7: Confidence Intervals
With a point estimate, we used a single number to
estimate a parameter.
We can also use a set of numbers to serve as
reasonable estimates for the parameter.
Example: Assume we have a sample of size 100 from a
p
Practice exam 1 of STAT 515
Section 002, Spring 2016
Instructor: Wang, Lianming
Name: _
Note: You have 75 minutes for this exam. Please show your work in order to get full credits.
1. (10 points) Circle the most appropriate answer.
1) It is known that eve
STAT 515 - Chapter 6: Sampling Distributions
Definition: Parameter = a number that characterizes a
population (example: population mean ) its typically
unknown.
Statistic = a number that characterizes a sample
_
(example: sample mean X) we can calculate i
STAT 515 - Chapter 5: Continuous Distributions
Probability distributions are used a bit differently for
continuous r.v.s than for discrete r.v.s.
Continuous distributions typically are represented by a
probability density function (pdf), or density curve.
STAT 515 - Chapter 4: Discrete Random Variables
Random Variable: A variable whose value is the
numerical outcome of an experiment or random
phenomenon.
Discrete Random Variable : A numerical r.v. that takes
on a countable number of values (there are gaps
STAT 515 - Chapter 4: Discrete Random Variables
Random Variable: A variable whose value is the
numerical outcome of an experiment or random
phenomenon.
Discrete Random Variable : A numerical r.v. that takes
on a countable number of values (there are gaps
STAT 515, Statistical Methods I - Spring 2011
Instructor:
David Hitchcock, assistant professor of statistics
209A LeConte College
Phone: 777-5346
Email: hitchcock@stat.sc.edu
Course Web Page: http:/www.stat.sc.edu/~hitchcock/stat515.html
(Also accessible
Formula Sheet Test 2 STAT 515
For X Poisson():
P (x) =
x e
x!
For X Uniform(c,d):
P (a < X < b) =
Z=
ba
c+d
dc
, =
, =
dc
2
12
X
, X = Z +
X
/ n
Z=
x t/2 (s/ n),
where t/2 based on n 1 df
p(1 p)
n
p z/2
(n 1)s2 (n 1)s2
,
2 2
2/2
/
1
s2 /s2
12
s2 /s2
1
1
Formula sheet for mid-term exam 1
n
k
=
n!
k!(nk)!
P (A B) = P (A) + P (B) P (A B)
S
T
P (Ac ) = 1 P (A)
P (A B) = P (A) P (B|A)
T
P (A) = P (B)P (A|B) + P (B c )P (A|B c )
P (B|A) =
P (B)P (A|B)
P (B)P (A|B)+P (B c )P (A|B c )
Expected value: = E
Homework No. 2 (STAT515-Fall 2011) 1.12. (24 points) Except for d, which is qualitative, all the others are quantitative. Comment: Some of you argued that "b. High school class rank" is qualitative. One reason you presented to me is that it is not as mean
Homework #3 (STAT 515-Fall 2011) 2.10. (8 points) a. The variable is "most salient role". The categories are given in the first column of the table. b. Frequencies. c.
Roles for Elderly
400 300 Count 200 100 0
nd rie F t e er en t iv ak ar la p em r e nd
Homework 4 (STAT515, Fall 2011) 2.110 (4 points) According to the provided statistics, the average scores is 279, 25% of the eighth graders scored lower than 255, 75% lower than 304, and 10% higher than or equal to 324 (i.e., 90% below 324). 2.114. (4 poi
Answers to some exercises in chapter 3 and 4 (STAT 515, Fall 2011) 3.66. a. Because A and B are mutually exclusive, P (A B) = P (A) + P (B) = 0.85. b. By the definition of mutually exclusive events, P (A B) = 0. c. P (A|B) = P (A B)/P (B) = 0, since the n
Solution to Homework 5 (STAT515, Fall 2011) 4.60. (20 points) a. (5 points) One needs to assume that the sample of five brands forms an independent sample from a big population of bottled-water brands. Then one can view the experiment, "inspecting these f
Solution to Homework 6 (STAT515, Fall 2011) 5.24. (8 points) a. 0.0721; c. 0.2434; f. 0.9233; g. 0.9901. 5.28. (8 points) a. -1.75; b. 1.96; e. 0.83; f. 2.50. 5.30. (6 points) a. 0.3830; c. 0.1525; f. 0.9545. 5.32. (8 points) a. 30; b. 14.32; c. 40.24; d.
Solution to Homework 7 (STAT515, Fall 2011) 7.10. (15 points) Given n = 90 (large sample), x = 25.9, and s = 2.7, a. A 95% confidence interval for is given by s 2.7 x z0.025 = 25.9 1.96 (25.34, 26.46). n 90 b. A 90% confidence interval for is given by s 2
Solution to Homework 8 (STAT515, Fall 2011) 8.26 (15 points) a. The rejection region of a large-sample lower-tailed test at a significance level of = 0.01 is given by (-, -z0.01 ) (-, -2.33). x - 0 19.3 - 20 -0.40. = b. z = s/ n 11.9/ 46 c. Notice that th
Solution to some problems in chapter 10 10.22. a. The completed ANOVA table is given in Table 1.
Table 1: The complete ANOVA table for Problem 10.22. Source Treatments Error Total df 6 SS 18.4 MS 3.0667( 18.4/6) F 4.0051( 3.0667/0.7657)
35(=41 - 6) 26.8(=
STAT 515 - Chapter 3: Probability
Basic Definitions
Experiment: A process which leads to a single outcome
(called a sample point) that cannot be predicted with
certainty.
Sample Space (of an experiment): The collection of all
the possible outcomes (or sam