Exam 2 Study Guide
Pooling A better estimate of common proportion and its standard deviation are possible when
data from different sources are believed to be homogeneous. The data are combined, or pooled,
into a single group for the purpose of estimating
STAT W1211
Lecture 2
there is sufficient evidence to conclude that the proportion of those who are unscreened who die
is lower than that for those who are screened.
Alternatively, we can find the p-value = P(Z > 2.17) = 1P(Z < 2.17) = 0.0150 < = 0.05, so
STAT W1211
Lecture 1
1) You suspect the die a player roles may be unfair. To check, you roll it
60 times, recording the number of times each face appears. The results are summarized in the
table below:
Is there evidence that the die is unfair?
Solution: 2
Exam 1 Study Guide
Independence the sampled values must be independent of each other
Sample Size assumption sample size must be sufficiently large
Conditions
Randomization the data values must be samples randomly, or the concept of a sampling
distribution
Lecture 5
However, since n is so large, we can consider this a z statistic.
At = 0.05, the one-tailed z critical value is -1.645.
Since our zstat < zcrit, , we reject the null hypothesis and say there is sufficient evidence to
conclude that the true mean
Random Variables
Prob Distr for Discrete rv
Expected Values
Discrete RV
Chapter 3: Discrete Random Variables and
Probability Distributions
Version 1 1/28/2016
Chapter 3: Discrete Random Variables and Probability Distribu
Random Variables
Prob Distr for Di
Sample Space and Events
Axions, Int., Prop. of Prob.
Counting techniques
Conditional Probability
Independence
Additional Reading Materials
Chapter 2: Probability
Version 1,( 1/21/2016)
Chapter 2: Probability
Sample Space and Events
Axions, Int., Prop. of
Introduction
Populations, Samples and Processes
Pictorial and Tabular Methods in Descriptive Statistic
Measures of Location
Measures of Variability
Chapter 1
Overview and Descriptive Statistics
Chapter 1
Introduction
Populations, Samples and Processes
Pic
PRACTICE PROBLEMS FOR CHAPTER 5
Let X and Y be two continuous random variables with joint pdf:
(, ) =
0
0 1, 0 < 1, + 1
where k is a constant.
1. What is k so that f(x,y) is a legitimate joint pdf?
2. What is E(XY)?
3. What is the covariance of (X,Y)?
Pra
Jointly Distributed Random Variables
Expected Values, Covariance and Correlation
Statistics and Their Distributions
Distribution of Sample Mean
Distribution of a Linear Combination
Chapter 5:Joint Probability Distributions and
Random Samples
Version 1,( 2
Summation
Set Theory
Binomial expansion
Basic Integral Results
Multiple Integral
Introduction to Statistics with Calculus
Math Review
Introduction to Statistics with Calculus Math Review
Summation
Set Theory
Binomial expansion
Basic Integral Results
Multi
Obesity in America
Nate Brennand
Morgan Caglianone
Alix Cook
Obesity and Overweight Rates
We seek to observe how various factors
are correlated to with overweight and
obesity rates from state to state.
By analyzing these statistics we wish to
provide insi
Lecture 3
(Came Late)
Alternatively, we can find the p-value = P(Z < 1.15) + P(Z > 1.15) = 2 P(Z < 1.15) = 0.2501
> = 0.05, so fail to reject the null hypothesis.
7) A 1992 poll conducted by the University of Montana classified participants party affiliat
STAT W1211
Lecture 4
9) Data show that the average height of an American has increased throughout the years. A
linear regression between year and height is produced. Person 1 says the mean height in 2020
will be x.
How can we test whether or not his claim
STAT W1211
Lecture 8
Drug S (standard). The results were as follows: 30 out of 300 patients on Drug E and 60 out of
300 patients on Drug S had an upper respiratory infection.
a.) Did Drug E significantly reduce the risk of infection?
Solution: Two-sample
STAT
Lecture 6
Solution: Two-sample test of proportions
Let p1 = the true proportion of males who express confidence, p2 that for females.
H0 :p1 =p2
Ha :p1 =p2
Since we are testing the hypothesis of equal proportions, we must pool the proportions
If the
Lecture 9
At = 0.05, the chi-square critical value is 9.488.
Since our 2stat < 2crit, we fail to reject the null hypothesis and say there is not sufficient
evidence to conclude Student type and day of week depend on each other.
4) In a Gallup survey of ad
STAT W1211
Lecture 7
Under the null hypothesis, this will have a t distribution with n-1 degrees of freedom
We then reject for extreme values of tstat in relation to the one-tailed critical value.
*TEST TWO*
1) Suppose we performed a test of significance
Final Prep Multiple Choice Questions
Q1
Q2
Q3
Q4
Q5
Q6
Q7
Q8
Q9
Q10
Q 11
Q12
A large company that produces allergy medications claims that Americans lose an average of 40 hours of work
to problems related to seasonal allergies. A consumer advocacy group b
Probability Density Functions
Cumulative DF and Expected Values
Normal Distribution
Exponential Distribution
Gamma Distribution
Chi-Square distribution
Probability Plot
Chapter 4: Continuous RV and Probability
Distributions
January 26, 2016
Chapter 4: Con