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
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
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
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.
Examp
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 relations
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 (call
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 i
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
p
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
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) Circ
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
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
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
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
STAT 515, Statistical Methods I - Spring 2011
Instructor:
David Hitchcock, assistant professor of statistics
209A LeConte College
Phone: 777-5346
Email: [email protected]
Course Web Page: http:/ww
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
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|
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. O
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
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 th
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
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
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.
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)
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
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 3.06
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 experimen