Chapter 10: Sampling Distributions
What is a sampling distribution?
The sampling distribution is the theoretical probability distribution of the values of a statistic that results when
all possible random samples of a particular size are drawn from a popu
Sections 10-3 and 10-4: The Central Limit Theorem
Recall: The objective of statistics is to make decisions (or inferences) about populations in light of variation.
To accomplish this, we sample and then attempt to draw our conclusions.
Sampling results ar
Confidence Intervals for
Interval Estimation
An interval estimate of a population parameter consists of two bounds L and U within which the parameter is
estimated to lie:
where L is the lower bound and U is the upper bound.
The probability that a correct
1-Proportion Hypothesis Tests: For use with Binomial Experiments
Chapter 11: Testing Hypotheses about proportions
Comparing a population proportion to some standard:
HA: population proportion greater than some value
HA: population proportion less than som
Types of Hypothesis Testing:
For the following examples, c represents any constant.
I. One-sided Alternative
a. Greater Than
H:
A
H:
0
b. Less Than
H:
A
H:
0
II. Two-Sided Alternative
H:
A
H:
0
Alternate hypothesis: process average is greater than c
Null
Summary of the Hypothesis Tests run in Math 3340
Chapter 13: Testing Hypotheses (1-sample tests)
1-proportion test
Comparing a population proportion to some standard:
HA: population proportion greater than some value
HA: p > some value
HA: population prop
Chapter 14: Testing Differences between Two Population Means
(The data utilized in this document is found in the Minitab file on Blackboard entitled: Chapter 14
Examples.MTW
I. Comparison of the means of two independent samples The 2 Sample t-test.
Indepe
Introduction to Hypothesis Testing
I.
Fundamentals of Hypothesis Testing
Most people want to make the proper decision when solving problems or performing research. There are times
that we are required to prove that a product is improved. We may be asked t
Which type of test should I run? (Paired t-test vs. 2 Sample Independent t-test)
1. The management of Discount Furniture designed an incentive plan for salespeople. To evaluate this
innovative plan, 12 sales people were selected at random, and their weekl
Which test should I run?
1. A farmer is concerned that a change in fertilizer to an organic variant might change his crop yield. He
subdivides 6 lots and uses the old fertilizer on one half of each lot and the new fertilizer on the other
half. The followi
Chapter 15 Inference for Counts: Chi-Square Tests
Hypothesis tests covered in Chapter 15
Comparing two population proportions:
HA: population proportion 1 greater than population proportion 2
HA: population proportion 1 less than population proportion 2
H
For each of the following problems:
Classify the problem as 1-Proportion, 2-Proportion, Chi-Square Goodness of fit, or Chi-Square test for
independence.
a. Determine the research hypothesis.
b. Determine the null hypothesis.
1. Suppose a new product was
Chapter 15 Inference for Counts: Chi-Square Tests
Section 15-6: The Chi-Square Test of Independence
These tests are run to compare two categorical variables. You will use them often in survey analysis.
Suppose that you wanted to determine if whether or no
Chapter 6: Correlation and Linear Regression
WHENEVER YOU BEGIN TO INVESTIGATE THE RELATIONSHIP BETWEEN TWO VARIABLES, START THE
INVESTIGATION BY LOOKING AT A SCATTER-PLOT.
Scatter-plots
A scatter plot, which plots one quantitative variable against anothe
Chapter 16 Notes:
HYPOTHESIS TEST (Inference for Regression)
Is the Y variable related to the X variable?
HA: 0
[Y is related to X.]
Ho: = 0
[Y is not related to X.]
We assume there is no relationship unless the data demonstrate that there is one.
Assumpt
Chapter 18 - Multiple Regression
Linear Regression Model:
b0 is the y-intercept of the least squares regression line.
b1 is the slope of the least squares regression line.
Multiple Regression Model:
Each value (bk) is the estimated coefficient of its corr
Chapter 21: The Theory behind ANOVA (Analysis of Variance)
When we need to compare more than 2 sample averages, the correct method to do so is to use Analysis of
Variance (ANOVA).
The hypotheses when running an ANOVA are:
HA: At least one mean is differen
Chapter 11: Confidence Intervals for p (the true population proportion)
Note: this is for use with binomial random variables.
The number of sample observations with the characteristic of interest in a simple random sample of size n is
called the sample fr