Unit 1 Descriptive Statistics & Basic Probability

Math 131 Notes
Math 131 Notes 1
Unit 1 Descriptive Statistics & Basic Probability 1
Chapter 1: Introduction 1
Section 1.1: Overview of Statistics (p 2) 1
Section 1.2: Data Classification (p 8) 1
Section 1.3 Experimental Design (p 15) 1
Generating random numbers in Minitab 2
Sorting numbers in Minitab (Manual p 11) 2
Using Minitab to select a random sample from a dataset stored in
columns 2
Generating a Sequential set of numbers in Minitab and then
selecting randomly from them (Manual p 8) 2
Chapter 2: Descriptive Statistics 2
Section 2.1 Frequency Distributions and their Graphs (p 32) 2
Constructing a Histogram in Minitab (Manual p 37) 3
Construction a Frequency Polygon in Minitab (Manual p 51) 4
Constructing an Ogive in Minitab (Manual p 54) 4
Section 2.2 More Graphs and Displays (p 46) 5
Constructing a stem-and-leaf chart in Minitab (Manual p 45) 6
Constructing a Pie Chart in Minitab(Manual p 25) 7
Constructing a Pareto (Bar) Chart in Minitab (Manual p 15) 9
Section 2.3 Measures of Central Tendency (p 57) 10
Finding Measures of Central Tendency in Minitab (Manual p 67) 11
Using Minitab to Obtain Frequency of Individual Variables 11
Section 2.4 Measures of Variation (p 70) 11
Finding Measures of Variation in Minitab 12
Section 2.5 Measures of Position (p 87) 12
Finding Quartiles in Minitab (Manual p 88) 13
Constructing a Boxplot in Minitab (Manual p 90) 15
Using Minitab to Compute z-scores (Manual p 86) 16
Chapter 3 Probability (p 109) 16
Section 3.1 Basic Concepts of Probability 16
Unit 2 Probability & Probability Distributions 18
Section 3.2 Conditional Probability and the Multiplication Rule (p
121) 18
Section 3.3 The Addition Rule 18
Simulating the Birthday Problem in Minitab 19
Section 3.4 Counting Principles (p 140) 19
Chapter 4 Discrete Probability Distributions (p 161) 21
Section 4.1 Probability Distributions (p 162) 21
Section 4.2 Binomial Distributions (p 174) 22
Constructing a binomial Distribution using Minitab (Manual p 128)
25
Chapter 5 Normal Probability Distributions (p 205) 26
Section 5.1 Introduction to Normal Distributions (p 206) 26
Section 5.2 The Standard Normal Distribution (p 214) 26
Section 5.3 Normal Distributions: Finding Probabilities 26
Using Minitab to find the probability that a normally distributed
random variable is less than a specified value (Manual p 157) 28
Using Minitab to find the probability that a normally distributed
random variable is between two specified values (Manual p 159) 28
Section 5.4 Normal Distributions: Finding Values (p 229) 28
Section 5.5 The Central Limit Theorem (p 238) 29
Section 5.6 Normal Approximations to Binomial Distributions (p 251)
30
Unit 3 Inferential Statistics 32
Chapter 6 Confidence Intervals (p 269) 32
Section 6.1 Confidence Intervals for the Mean (Large Samples) 32
Using Minitab to find the Confidence Interval with a Sample in a
Column for a Normal Distribution (Manual p 183) 33
Using Minitab to find the Confidence Interval with Summarized
Data for a Normal Distribution 34
Determining Sample Size (p 276) 34
Section 6.2 Confidence Intervals for the Mean (Small Samples) (p
284) 34
Summary of when the normal distribution or the t-distribution can be
used (p 288) 35
Using Minitab to find the Confidence Interval for a t-
Distribution with the Sample in a Column (Manual p 193) 35
Using Minitab to find the Confidence Interval with Summarized
Data for a t-Distribution 36
Section 6.3 Confidence Intervals for Population Proportions (p 293)
36
Chapter 7 Hypothesis Testing with One Sample 37
Section 7.1 Introduction to Hypothesis Testing (p 321) 37
Alternative Hypothesis 39
Area of Normal Curve 39
Section 7.2 Hypothesis Testing for the Mean (Large Samples) (p 334)
39
Using Minitab for Hypothesis testing for the mean with summarized
data from a large sample 40
Section 7.3 Hypothesis Testing for the Mean (Small Samples) (p 350)
41
Using Minitab to perform Hypothesis testing for the mean with
summarized data when the sample is small (Manual p 211) 41
Section 7.4 Hypothesis Testing for Proportions (p 360) 42
Using Minitab to perform Hypothesis testing for a proportion with
summarized data (Manual p 215) 42
Chapter 9 Correlation and Regression 43
Section 9.1 Correlation (p 442) 43
Using Minitab to draw a scatter plot (Manual p 93) 43
Using Minitab to find the Correlation Coefficient (Manual p 95)
45
Using Minitab to determine whether the correlation coefficient is
significant (Manual, p 95) 46
Section 9.2 Linear Regression (p 458) 46
Using Minitab to find the Least Squares Regression Equation (p
98) 47
Using Minitab to find the Regression equation and a predicted
value for the Old Faithful Data (p 460) 48
Using Minitab to draw the least squares regression line on the
scatter plot for the Old Faithful Data 49
Chapter 10 Chi-Square Tests and the F-Distribution (p 493) 49
Section 10.1 Goodness of Fit 49
Using Minitab to perform the Chi-Square Goodness-of-Fit Test
(Manual p 237) 50
Chi-Square with M&M's 51
Section 10.2 Independence (p 504) 52
Using Minitab to perform the Chi-Square Independence Test (Manual
p 242) 54
Unit 1 Descriptive Statistics & Basic Probability
Chapter 1: Introduction
Section 1.1: Overview of Statistics (p 2) . Data consists of information coming from observations, counts,
measurements, or responses. The singular of data is datum. (p 2)
. Statistics is the science of collection, organizing, analyzing and
interpreting data in order to make decisions. (p 3)
. A population is a collection of all outcomes, responses, measurements,
or counts that are of interest. (p 3)
. A sample is a subset of a population characteristic (p 3)
. A parameter is a numerical description of a population (p 4)
. A statistic is a numerical description of a sample characteristic (p
4)
. Descriptive Statistics is the branch of statistics that involves the
organization, summarization, and display of data. (p 5)
. Inferential statistics is the branch of statistics that involves using
a sample to draw conclusions about a population. A basic tool in the
study of inferential statistics is probability (p 5). Section 1.2: Data Classification (p 8) . Qualitative data consist of attributes, labels, or nonnumerical
entries. (p 8)
. Quantitative data consist of numerical entries or counts.
. Nominal level of measurement: qualitative (p 9)
. Ordinal level of measurement: qualitative or quantitative, can be
ordered, but differences are not meaningful
. Interval level of measurement: quantitative, can be ordered,
differences are meaningful, no inherent zero (e.g. 0 degrees) (p 10)
. Ratio level of measurement: quantitative, can be ordered, differences
are meaningful, inherent zero (e.g. 0 dollars) Section 1.3 Experimental Design (p 15) Guidelines for designing a statistical study (p 15)
1. Identify the variable(s) of interest (the focus) and the population of
study.
2. Develop a detailed plan for collecting data. If you use a sample, make
sure it is representative.
3. Collect the data
4. Describe the data using descriptive techniques.
5. Interpret the data and make decisions about the population using
inferential statistics.
6. Identify any possible errors. Data can be collected as follows (p 15-16)
. Census: A count or measure of the entire population
. Sampling: A count or measure of part of the population
. Simulation: Using a mathematical or physical model
. Experiment: A treatment is applied to part of a population and
responses are observed. A second part of the population is often used
as a control group and given no treatment or a placebo Sampling techniques: (p 17-19)
. Random sample: Select the sample randomly from the entire population
. Stratified sample: break population into subsets called strata (e.g.
ethnicity) and take random samples from each strata.
. Cluster sample: break population into groups called clusters (e.g. zip
codes) then randomly select clusters and select all the members of the
each cluster.
. Systematic sample: Assign a number to each member of the population,
randomly pick a number, then start with that number and choose at the
same interval from it. A convenience sample is not reliable! Generating random numbers in Minitab Calc->Random Data->Integer, Generate Enter number of random numbers (e.g.
sample size), Store in column(s), C1, Minimum of: 1, Maximum of Population
Size
Note, this way of generating random numbers can give repeats. Also, this
method is not described in the Minitab Manual. An easy way to eliminate
repeats is to sort the numbers so that the repeats appear sequentially,
then delete the