Interpreting Confidence Intervals
Submitted by gfj100 on Wed, 11/11/2009 - 13:43
The formula for confidence intervals remains the same:
Sample statistic Multiplier Standard error
In each of the scenarios described in this lesson, the sample statistic woul
Matched Pairs for Means
Submitted by gfj100 on Wed, 11/11/2009 - 13:42
Paired Data
Simply put, paired data involves taking two measurements on the same subjects, called repeated
sampling. Think of studying the effectiveness of a diet plan. You would weigh
Comparing Two Independent Proportions
Submitted by gfj100 on Wed, 11/11/2009 - 13:42
Example 3
In the same survey used for example 2, students were asked whether they think same sex
marriage should be legal. Well compare the proportions saying yes for mal
Comparing Two Independent Means - Unpooled and Pooled
Submitted by gfj100 on Wed, 11/11/2009 - 13:41
We determine whether to apply "pooled" or "unpooled" procedures by comparing the sample
standard deviations. RULE OF THUMB: If the larger sample standard
General Ideas for Testing Hypotheses
Submitted by gfj100 on Wed, 11/11/2009 - 13:40
Step 0: Assumptions
1. The samples must be independent and random samples.
2. If two proportions, then the two groups must consist of categorical responses. If two
means,
Comparing Two Groups
Submitted by gfj100 on Wed, 11/11/2009 - 13:39
Previously we discussed testing means from one sample or paired data. But what about situations
where the data is not paired, such as when comparing exam results between males and females
Errors, Practicality and Power in Hypothesis Testing
Submitted by gfj100 on Wed, 11/11/2009 - 13:16
Errors in Decision Making Type I and Type II
How do we determine whether to reject the null hypothesis? It depends on the level of
significance , which is
Hypothesis Testing for a Mean
Submitted by gfj100 on Wed, 11/11/2009 - 13:16
Quantitative Response Variables and Means
We usually summarize a quantitative variable by examining the mean value. We
summarize categorical variables by considering the proporti
Hypothesis Testing for a Proportion
Submitted by gfj100 on Wed, 11/11/2009 - 13:15
Ultimately we will measure statistics (e.g. sample proportions and sample means) and use them
to draw conclusions about unknown parameters (e.g. population proportion and p
Hypothesis Testing
Submitted by gfj100 on Wed, 11/11/2009 - 13:14
Previously we used confidence intervals to estimate some unknown population parameter. For
example, we constructed 1-proportion confidence intervals to estimate the true population
proporti
Using Software To Calculate Confidence Intervals
Submitted by gfj100 on Wed, 11/11/2009 - 12:51
Consider again the Class Survey data set (Class_Survey.MTW or Class_Survey.XLS) that
consists of student responses to survey given last semester in a Stat200 c
Constructing confidence intervals to estimate a population
mean
Submitted by gfj100 on Wed, 11/11/2009 - 12:50
Previously we considered confidence intervals for 1-proportion and our multiplier in our interval
used a z-value. But what if our variable of in
Constructing confidence intervals to estimate a population
proportion
Submitted by gfj100 on Wed, 11/11/2009 - 12:45
NOTE: the following interval calculations for the proportion confidence interval is dependent on
the following assumptions being satisfied
Toward Statistical Inference
Submitted by gfj100 on Wed, 11/11/2009 - 12:44
Two designs for producing data are sampling and experimentation, both of which should employ
randomization. As we have already learned, one important aspect of randomization is to
Review of Sampling Distributions
Submitted by gfj100 on Wed, 11/11/2009 - 12:01
In later part of the last lesson we discussed finding the probability for a continuous random
variable that followed a normal distribution. We did so by converting the observe
Sampling Distribution of the Sample Mean, xbar
Submitted by gfj100 on Wed, 11/11/2009 - 12:00
The central limit theorem states that if a large enough sample is taken (typically n > 30) then
the sampling distribution of is approximately a normal distributi
Sampling Distributions for Sample Proportion, p-hat
Submitted by gfj100 on Wed, 11/11/2009 - 11:59
If numerous repetitions of samples are taken, the distribution of
is said to approximate a
normal curve distribution. Alternatively, this can be assumed if
Normal Approximation to the Binomial
Submitted by gfj100 on Wed, 11/11/2009 - 10:45
Remember binomial random variables from last week's discussion? A binomial random variable
can also be approximated by using normal random variable methods discussed above
Finding Cumulative Probabilities
Submitted by gfj100 on Wed, 11/11/2009 - 10:43
Using the Standard Normal Table in the appendix of textbook or see a copy at Standard
Normal Table
Table A.1 in the textbook gives normal curve cumulative probabilities for st
Continuous Random Variable
Submitted by gfj100 on Wed, 11/11/2009 - 10:42
Density Curves
Previously we discussed discrete random variables, and now we consider the contuous type.
A continuous random variable is such that all values (to any number of decim
Binomial Random Variable
Submitted by gfj100 on Wed, 11/11/2009 - 10:41
This is a specific type of discrete random variable. A binomial random variable counts how often
a particular event occurs in a fixed number or tries. For a variable to be a binomial
Mean, also called Expected Value, of a Discrete Variable
Submitted by gfj100 on Wed, 11/11/2009 - 10:40
The phrase expected value is a synonym for mean value in the long run (meaning for many
repeats or a large sample size). For a discrete random variable
Probability Distributions: Discrete Random Variables
Submitted by gfj100 on Wed, 11/11/2009 - 10:39
For a discrete random variable, its probability distribution (also called the probability
distribution function) is any table, graph, or formula that gives
Random Variables
A random variable is numerical characteristic of each event in a sample space, or equivalently,
each individual in a population.
Examples:
The number of heads in four flips of a coin (a numerical property of each different
sequence of fli
THINK & PONDER!
Submitted by gfj100 on Wed, 11/11/2009 - 10:13
Given P(A) = 0.6, P(B) = 0.5, and P(A B) = 0.2.
Find P( ).
Work out your answer first, then click the graphic to compare answers.
Find P(A
).
Work out your answer first, then click the graphic
How do we check for independence?
Submitted by gfj100 on Wed, 11/11/2009 - 10:10
Recall that two events are independent when neither event influences the other. That is, knowing
that one event has already occurred does not influence the probability that t
Examples
Submitted by gfj100 on Wed, 11/11/2009 - 10:07
Example 1
The probability of a student getting an A in this course is 0.25 (Not True!) and the probability of
getting a B is 0.30 (again Not True!). What is the probability of getting an A or a B? Ac
Conditional Probability
Submitted by gfj100 on Wed, 11/11/2009 - 10:09
In the lesson on Examining Relationships we found conditional distributions from two-way
tables [for example, to find the percentage of students who did not smoked
cigarettes given gen
General Probability Rules
Submitted by gfj100 on Tue, 11/10/2009 - 16:55
Rule 1: The probability of an impossible event is zero; the probability of a certain event is one.
Therefore, for any event A, the range of possible probabilities is: 0 P(A) 1
Rule 2
Basic Principles of Statistical Design of Experiments
Submitted by gfj100 on Tue, 11/10/2009 - 16:29
Example
A group of college students believe that regular consumption of a special Asian tea could benefit
the health of patients in a nearby nursing home.