STAT412
Final Exam
Practice Questions
1. Researchers want to see if men have a higher blood pressure than women do. A study is planned in which the
blood pressures of 50 men and 50 women will be measured. What's the most appropriate research hypothesis ab
Terminology
Statistics is the science of collecting, summarizing, analyzing, and drawing conclusions from data.
One of the main objectives of statistics is to make an inference about a population of interest based on
information obtained from a sample of
Data Setting: A graduate student in Psychology was asked to grade 40 final exams, selected at
random from several large sections of an introductory course. The resulting scores are found below.
77
84
91
50
75
68
92
74
81
92
86
96
61
37
80
84
83
52
60
75
9
Probability
Suppose an experiment (such as dropping a thumbtack, tossing a coin, or selecting a candy from a bag of M&Ms) is
repeated many times. The relative frequency associated with an outcome (such as the tack landing with the point upward,
or heads r
Example of Calculating TypeII error and Power of the test
In this section, you will get some practice in calculating the probability of a type2 error for a hypothesis test.
Consider a test of H0: = 124 versus Ha: > 124. The test uses = 16, =0.05 and a s
Estimation of a Population Proportion,
A 100(1)% confidence interval for is
(z /2 )
NOTE: This interval is valid whenever
n and n(1 ) are both at least 5.
Properties of the sampling distribution of
1. The sampling distribution of
2. The standard deviat
How can we explore the association between two quantitative variables?
An association exists between two variables if a particular value of one variable is more likely to occur with
certain values of the other variable.
For higher levels of energy use, do
Introduction to Minitab
(Student and Professional Versions 15)
OVERVIEW
In this lab, you will become familiar with the general features of Minitab statistical analysis
software, as well as some specialized features for conducting introductory statistical
STAT412
Homework 1
Due Friday, September 4
1. A study of the effect of parents' smoking habits on the smoking habits of students in a high school produced the following
table.
Parents
Both parents smoke
One parent smokes
Neither parent smokes
Total
Studen
t Distribution
When x is the mean of a random sample of size n from a normal distribution with mean , the random
variable
t
x
s
n
has a probability distribution called a t distribution with n 1 degrees of freedom (df).
Properties of t Distributions
Let t
STAT412
Exam 1
PRACTICE QUESTIONS
Name_
Multiple choice questions:
1. If we are performing a hypothesis test of H 0: = 60 vs. Ha: > 60, the probability of rejecting H0 if
will be _ the probability of rejecting H0 if .
A) less than
B) greater than
C) equa
STAT412
Exam 2
Practice Questions
Questions 1 to 3: In the General Social Survey, respondents were asked what they thought was most important to
get ahead: hard work, lucky breaks, or both. Minitab output for 1026 respondents, by gender, is shown below:
E
OneFactor Analysis of Variance
The procedure is used when one is interested in comparing more than two means. The procedure is a generalization of
the pooledt test.
Example A researcher wants to compare three different methods for teaching reading.
Fact
STAT212
EXAMPLES
1. A local pizza restaurant and a local branch of a national chain are located across the street from a college campus.
The local pizza restaurant advertises that they deliver to the dormitories faster than the national chain. In order to
Analysis of Categorical Data
Hypothesis Test for a Population Proportion,
Ho: 0
Ha:
1. 0
2. 0
3. 0
z
T.S.
0
R.R. For a probability of a TypeI error
1. Reject Ho if z z
2. Reject Ho if z z
3. Reject Ho if z z/2 or if z z/2
Note: Under H0,
0 (1 0
TwoFactor Analysis of Variance
Here we look at applying twofactor analysis of variance where we interested in studying the effects of two
factors on a response variable.
Example A horticulturist wants to study the effects of four different pesticides on
Randomized Block Design
Block Design: A block is a group of experimental units or subjects that are known before the
experiment to be similar in some way that is expected to affect the response to the treatments. In a
block design, the random assignment o
Solution
What
Does It
Mean
The histogram in Printout 7.1
indicates that i is normally
distributed, that is, that the
possible sample mean IQs for
samples of four people have a
normal distribution.
‘?
FRI NTOIJT 7.1
Histogram of the sample means for
1000 s
Pooledt test in Minitab
Example Bowker and Lieberman (1972) gave the results for tests of two thermostats used in irons that were made by
an old supplier and a new supplier. Twenty three thermostats from each supplier were tested at a setting of 550 F. T
STAT 412 HW1 Solutions
1a. P(student smoke and at least one parent smoke) =
b. P(student smoke or 2 parents smoke) =
2. P(head or 6) =
1
2
1
6
+

1
2
*
180
1000
1
6
=
+
150
1000
= 0.15
330
1000
70
 1000
7
12
3a. P (A or C) = P(A) + P(C) P(A and C) = 0.4
Single Factor Analysis of Variance
Using MINITAB
EXAMPLE Some investigators think that the concentration (mg/ml) of a particular antigen in supernatant fluids could be related to
the onset of meningitis in infants. The accompanying data is typical of that
Lab assignment 2
Pearson Correlation Coefficient:
r
n xy ( x)( y )
n ( x 2 ) ( x ) 2 n( y 2 ) ( y ) 2
In Minitab:
Enter in data first
Stat
Basic statistics
variables you want to (here should be x and y)
ok
Correlation
click the
Least square line:
y
=
o 1
TwoFactor Analysis of Variance
Using MINITAB
EXAMPLE An experiment was performed to determine the effects of four different pesticides on the yield of fruit from three
different varieties of a citrus tree. Eight different trees were chosen from each vari
Comparing Two Population Means Using Independent Samples
Pooledt test
Definitions Two samples are independent if the sample values selected from one population are not related to or
somehow paired or matched with the sample values selected from the other
ChiSquare Test of Independence
H0: The two variables are independent
Ha: The two variables are dependent
Test Statistic:
(observedcel count expectedcel count)2
2=
expectedcel count
al
cel s
Rejection Region: Reject Ho if 2 >
2 , (r 1)(c1)
NOTE: This
Normal Probability Plot
Many statistical inference procedures require a normality assumption. One useful way of assessing the reasonableness of this
assumption is by constructing a normal probability plot (see p7677). If the plotted points fall approxima
STAT412
and Power Calculations
InClass Exercise
Suppose you want to test Ho: =1,000 against Ha: >1,000 using =.025. The population in question is
normally distributed with standard deviation 120. A random sample of size n=36 will be used.
a. Sketch the
Hypothesis Testing
Methods for making inferences about population parameters fall into one of two categories. Either we will
estimate the value of the population parameter of interest or we will test a hypothesis about the value of the
parameter.
With con