Chapter 5 Homework
Due: Feb 26, 2017
Case Study: Planning a Heart-Healthy Diet
Jackie is a 21-year-old health-conscious individual majoring in business. She recently learned that a diet
high in satura
ASSIGNMENT SOLVED
4. Why is a 99% confidence interval wider than a 95% confidence interval?
Answer. A 95% Confidence Interval would be narrower than a 99% Confidence Interval. This
occurs because the
American University of Afghanistan (AUAF)
Department of Math and Science
Statistics -1
Summer Semester 2015
Instructor: Asadullah Jawid (M. Sc. University of Bonn)
Email: [email protected]
Office: Fa
3-3 Cumulative Distribution Function
1
2
Example 3-7
3
3-4 Mean and Variance of a Discrete Random Variable
4
Example 3-9
5
6
Example 3-11
3-4 Mean and Variance of a Discrete
Random Variable
See exampl
2-2 Interpretations of Probability
2-2.1 Introduction
Probability
Used to quantify likelihood or chance
Repeat an Experiment many times, assume that each trial of the experiment results
in only one o
2-1 Sample Spaces and Events
2-1.1 Random Experiments
Controlled Variables
Input
Text
System
Output
Uncontrolled Variables
(noise)
Because of the uncontrollable inputs, the
same settings for the contr
Conditional Probability Distributions
Two Discrete Random Variables
When two random variables are defined in a random experiment,
knowledge of one can change the probabilities that we associate
with t
4-5 Continuous Uniform Random Variable
Definition
4-5 Continuous Uniform Random Variable
Mean and Variance
4-5 Continuous Uniform
Random Variable
4-5 Continuous Uniform Random Variable
4-6 Normal Dist
3-1 Random Variables
- Random (Stochastic) experiment is defined as that whose
outcome cannot be predicted for sure
- The occurrence of a specific outcome of a stochastic process
( or an experiment) i
2-6 Independence
Definition (two events)
Also,
Example 2-29
What is P(B)?
Does P(B|A) = P(B)?
2
Example 2-30 Text
D denotes the event that a part is defective
F denotes the event that a part has a sur
3-9 Poisson Distribution
A widely used discrete probability distribution; Consider the following conditions:
- p is very small and approaches 0
example: a 100 sided dice instead of a 6 sided dice, p =
Continuous Random Variable:
is a random variable with an interval ( either
finite or infinite) of real numbers for its range
Examples: length, electric current, time, temperature,.
The probability dis
1
2
4
5
6
Example
Example
4-7 Normal Approximation to the
Binomial and Poisson Distributions
The normal distribution can be used to approximate the binomial
distribution when n is large.
For large va
4-8 Exponential Distribution
f(x)
x
2
4-8 Exponential Distribution
The exponential distribution is sometimes used to model the waiting
time to an event. It turns out that the exponential distribution
Independence:Two Discrete Random Variables
Joint and marginal probability
distributions of X and Y
Conditional probability distribution
of Y given X=x
Independence:Two Continuous Random Variables
3
Ex
Joint Probability Distribution,
2
Example: (Jointly discrete RV),
consider
The joint probability mass function is the function f XY(x,y)=P(X=x,
Y=y), for example, fXY(129,15)= 0.12
3
4
5
6
Example:
8
For a finite population with N equally likely values, the probability mass function is
f(xi) = 1/N and the mean is
The greater the amount of variability in the data, the larger in absolute magnitude o
1
- Often in practice we are interested in drawing valid conclusions about a large group
of individuals or objects.
- Instead of examining the entire group, called the population, which may be
difficu
Chapter 12
Inference on Categorical Data
12.1 Goodness of Fit Test
1. These procedures are for testing whether sample data are a good fit with a hypothesized
distribution.
2. The 2 goodness of fit tes
Chapter 11
Inferences on Two Samples
11.1 Inferences about Two Means: Dependent Samples
1. independent
2.
dependent
3. Since the researcher claims the mean of population 1, 1 , is less than the mean o
Chapter 10
Testing Claims Regarding a Parameter
10.1 The Language of Hypothesis Testing
1. A Type I error is the error of rejecting H 0 when in fact H 0 is true. A Type II error is the
error of not re
Chapter 9
Estimating the Value of a Parameter Using Confidence Intervals
9.1 The Logic in Constructing Confidence Intervals about a Population
Mean Where the Population Standard Deviation is Known
1.
Chapter 8
Sampling Distributions
8.1 Distribution of the Sample Mean
1. The sampling distribution of a statistic (such as the sample mean) is the probability
distribution for all possible values of th
Chapter 7
The Normal Probability Distribution
7.1 Properties of the Normal Distribution
1. For the graph to be that of a probability density function,
(1) The area under the graph over all possible va
Chapter 5
Probability
5.1 Probability Rules
1. Empirical probability is based on the outcome of a probability experiment and is
approximately equal to the relative frequency of the event. Classical pr
Chapter 4
Describing the Relation between Two Variables
4.1 Scatter Diagrams and Correlation
1. Univariate data measures the value of a single variable for each individual in the study.
Bivariate data
Chapter 3
Numerically Describing Data from One Variable
3.1 Measures of Central Tendency
1. A statistic is resistant if it is not sensitive to extreme data values. The median is resistant
because it i