This document discusses hypothesis testing of claims about population standard deviations and variances. It provides the steps to conduct hypothesis tests of such claims using the chi-square distribution. The chi-square test can be used to test if a sample variance or standard deviation is significantly different from a claimed population variance or standard deviation. Examples show how to identify the null and alternative hypotheses, calculate the test statistic, find the critical value, and make a decision to reject or fail to reject the null hypothesis based on the test statistic and critical value.
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Chapter 9: Inferences from Two Samples
9.4: Two Variances or Standard Deviations
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Chapter 8: Hypothesis Testing
8.2: Testing a Claim About a Proportion
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Chapter 9: Inferences from Two Samples
9.1: Inferences about Two Proportions
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Chapter 9: Inferences from Two Samples
9.4: Two Variances or Standard Deviations
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Chapter 8: Hypothesis Testing
8.2: Testing a Claim About a Proportion
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Chapter 9: Inferences from Two Samples
9.1: Inferences about Two Proportions
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Elementary Statistics Practice Test 4
Module 4:
Chapter 8, Hypothesis Testing
Chapter 9: Two Populations
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Chapter 4: Probability
4.3: Complements and Conditional Probability, and Bayes' Theorem
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Chapter 7: Estimating Parameters and Determining Sample Sizes
7.3: Estimating a Population Standard Deviation or Variance
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Chapter 10: Correlation and Regression
10.1: Correlation
Hypothesis testing and estimation are used to reach conclusions about a population by examining a sample of that population.
Hypothesis testing is widely used in medicine, dentistry, health care, biology and other fields as a means to draw conclusions about the nature of populations
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Chapter 10: Correlation and Regression
10.2: Regression
Solution to the Practice Test 3A, Chapter 6 Normal Probability DistributionLong Beach City College
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Elementary Statistics Practice Test 3
Practice Test Chapter 6 (Normal Probability Distributions)
Chapter 6: Normal Probability Distributions
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Chapter 5: Discrete Probability Distribution
5.1: Probability Distribution
Chapter 6 part2-Introduction to Inference-Tests of Significance, Stating Hyp...nszakir
Mathematics, Statistics, Introduction to Inference, Tests of Significance, The Reasoning of Tests of Significance, Stating Hypotheses, Test Statistics, P-values, Statistical Significance, Test for a Population Mean, Two-Sided Significance Tests and Confidence Intervals
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Elementary Statistics Practice Test 3
Module 2: Chapter 6 - Normal Probability Distribution
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Elementary Statistics Practice Test 2 Solutions
Chapter 4: Probability
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Chapter 8: Hypothesis Testing
8.1: Basics of Hypothesis Testing
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Elementary Statistics Practice Test 4
Module 4:
Chapter 8, Hypothesis Testing
Chapter 9: Two Populations
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Chapter 4: Probability
4.3: Complements and Conditional Probability, and Bayes' Theorem
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Chapter 7: Estimating Parameters and Determining Sample Sizes
7.3: Estimating a Population Standard Deviation or Variance
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Chapter 10: Correlation and Regression
10.1: Correlation
Hypothesis testing and estimation are used to reach conclusions about a population by examining a sample of that population.
Hypothesis testing is widely used in medicine, dentistry, health care, biology and other fields as a means to draw conclusions about the nature of populations
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Chapter 10: Correlation and Regression
10.2: Regression
Solution to the Practice Test 3A, Chapter 6 Normal Probability DistributionLong Beach City College
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Elementary Statistics Practice Test 3
Practice Test Chapter 6 (Normal Probability Distributions)
Chapter 6: Normal Probability Distributions
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Chapter 5: Discrete Probability Distribution
5.1: Probability Distribution
Chapter 6 part2-Introduction to Inference-Tests of Significance, Stating Hyp...nszakir
Mathematics, Statistics, Introduction to Inference, Tests of Significance, The Reasoning of Tests of Significance, Stating Hypotheses, Test Statistics, P-values, Statistical Significance, Test for a Population Mean, Two-Sided Significance Tests and Confidence Intervals
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Elementary Statistics Practice Test 3
Module 2: Chapter 6 - Normal Probability Distribution
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Elementary Statistics Practice Test 2 Solutions
Chapter 4: Probability
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Chapter 8: Hypothesis Testing
8.1: Basics of Hypothesis Testing
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Chapter 8: Hypothesis Testing
8.3: Testing a Claim About a Mean
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Chapter 8: Hypothesis Testing
8.4: Testing a Claim About a Standard Deviation or Variance
Int 150 The Moral Instinct”1. Most cultures agree that abus.docxmariuse18nolet
Int 150
“The Moral Instinct”
1. Most cultures agree that abusing innocent people is wrong. True or false
2. Young children have a sense of morality. True or false (example)?
3. Emotional reasoning trumps rationalizing. True or false (explain)
4. According to the article, psychopathy or moral misbehavior (like rape) is more environmental than genetic. True or false (example)
5. Explain the point about the British schoolteacher in Sudan.
6. Name three things anthropologists believe all people share, in addition to thinking it’s bad to harm others and good to help them.
a.
b.
c.
7. What is reciprocal altruism?
8. How does the psychologist Tetlock explain the outrage of American college students at the thought that adoption agencies should place children with couples willing to pay the most?
9. Discuss: A love for children and sense of justice is just an expression of our innate sense of preserving our genes for future generations (Darwin)
10. What does the author warn about the arguments regarding climate change?
Hypothesis Testing
(Statistical Significance)
1
Hypothesis Testing
Goal: Make statement(s) regarding unknown population parameter values based on sample data
Elements of a hypothesis test:
Null hypothesis - Statement regarding the value(s) of unknown parameter(s). Typically will imply no association between explanatory and response variables in our applications (will always contain an equality)
Alternative hypothesis - Statement contradictory to the null hypothesis (will always contain an inequality)
The level of significant (Alpha) is the maximum probability of committing a type I error. P(type I error)= alpha
Definitions
Rejection (alpha, α) Region:
Represents area under the curve that is used to reject the null hypothesis
Level of Confidence, 1 - alpha (a):
Also known as fail to reject (FTR) region
Represents area under the curve that is used to fail to reject the null hypothesis
FTR
H0
α/2
α/2
3
1 vs. 2 Sided Tests
Two-sided test
No a priori reason 1 group should have stronger effect
Used for most tests
Example
H0: μ1 = μ2
HA: μ1 ≠ μ2
One-sided test
Specific interest in only one direction
Not scientifically relevant/interesting if reverse situation true
Example
H0: μ1 ≤ μ2
HA: μ1 > μ2
4
Example: It is believed that the mean age of smokers in San Bernardino is 47. Researchers from LLU believe that the average age is different than 47.
Hypothesis
H0:μ = 47
HA: μ ≠ 47
μ = 47
α /2 = 0.025
Fail to Reject (FTR)
α /2 = 0.025
5
Three Approaches to Reject or Fail to Reject A Null Hypothesis:
1a. Confidence interval
Calculate the confidence interval
Decision Rule:
a. If the confidence interval (CI) includes the null, then the decision must be to fail to reject the H0.
b. If the confidence interval (CI) does not include the null, then the decision must be to reject the H0.
6
1b. Confidence interval to compare groups
Calculate the confidence interval for each gro.
Statistics practice for finalBe sure to review the following.docxdessiechisomjj4
Statistics practice for final
Be sure to review the following and have this information handy when taking Final GHA:
· Calculating z alpha/2 and t alpha/2 on Tables II and IV
· Find sample size for estimating population mean. Formula 8.3 p. 321 OCR.
· Stating H0 and H1 claims about variation and about the mean. Chapter 9 OCR.
· Type I and Type II errors p. 345 OCR.
· Confidence Interval for difference between two population means. Chapter 10 OCR p. 428
· Pooled sample standard deviation. Chapter 10 OCR p. 397
· What do Chi-Square tests measure? How are their degrees of freedom calculated? Chapter 12 OCR
· Find F test statistic using One-Way ANOVA.xls Be sure to enable editing and change values to match your problem. One-Way ANOVA.xls
· Find equation of regression line used to predict. To do on Excel, go to a blank worksheet, enter x values in one column and their matching y values in another column. Click Insert – Select Scatterplot. Right click any one of the points (diamonds) on the graph. Left click “Add a Trendline.” Check “Display Equation on Chart” box. Regression equation will appear on chart. Try it here with No. 20 below.
Practice Problems
Chapter 8 Final Review
1) In which of the following situations is it reasonable to use the z-interval
procedure to obtain a confidence interval for the population mean?
Assume that the population standard deviation is known.
A. n = 10, the data contain no outliers, the variable under consideration is
not normally distributed.
B. n = 10, the variable under consideration is normally distributed.
C. n = 18, the data contain no outliers, the variable under consideration is
far from being normally distributed.
D. n = 18, the data contain outliers, the variable under consideration is
normally distributed.
Find the necessary sample size.
2) The weekly earnings of students in one age group are normally
distributed with a standard deviation of 10 dollars. A researcher wishes to
estimate the mean weekly earnings of students in this age group. Find the
sample size needed to assure with 95 percent confidence that the sample
mean will not differ from the population mean by more than 2 dollars.
Find the specified t-value.
3) For a t-curve with df = 6, find the two t-values that divide the area under
the curve into a middle 0.99 area and two outside areas of 0.005.
Provide an appropriate response.
4) Under what conditions would you choose to use the t-interval procedure
instead of the z-interval procedure in order to obtain a confidence
interval for a population mean? What conditions must be satisfied in
order to use the t-interval procedure?
CHAPTER 8 Answers
1) B
2) 97
3) -3.707, 3.707
4) When the population standard deviation is unknown, the t-interval procedure is used instead of the
z-interval procedure. The t-interval procedure works provided that the population is normally
distributed or the.
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Elementary Statistics Practice Test 4
Chapter 9: Inferences about Two Samples
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Elementary Statistics Practice Test 4
Chapter 8: Hypothesis Testing
Solution to the practice test ch 10 correlation reg ch 11 gof ch12 anovaLong Beach City College
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Elementary Statistics Practice Test 5
Module 5
Chapter 10: Correlation and Regression
Chapter 11: Goodness of Fit and Contingency Tables
Chapter 12: Analysis of Variance
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Elementary Statistics Practice Test 5
Module 5
Chapter 10: Correlation and Regression
Chapter 11: Goodness of Fit and Contingency Tables
Chapter 12: Analysis of Variance
Solution to the practice test ch 8 hypothesis testing ch 9 two populationsLong Beach City College
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Elementary Statistics Practice Test 4
Module 4:
Chapter 8, Hypothesis Testing
Chapter 9: Two Populations
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Elementary Statistics Practice Test 3
Practice Test Chapter 6 (Normal Probability Distributions)
Chapter 6: Normal Probability Distributions
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Elementary Statistics Practice Test 2
Chapter 4: Probability
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Elementary Statistics Practice Test 1
Module 1: Chapters 1-3
Chapter 1: Introduction to Statistics.
Chapter 2: Exploring Data with Tables and Graphs.
Chapter 3: Describing, Exploring, and Comparing Data.
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Elementary Statistics Practice Test 1
Module 1: Chapters 1-3
Chapter 1: Introduction to Statistics.
Chapter 2: Exploring Data with Tables and Graphs.
Chapter 3: Describing, Exploring, and Comparing Data.
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Chapter 12: Analysis of Variance
12.2: Two-Way ANOVA
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Chapter 12: Analysis of Variance
12.1: One-Way ANOVA
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Chapter 11: Goodness-of-Fit and Contingency Tables
11.2: Contingency Tables
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Chapter 11: Goodness-of-Fit and Contingency Tables
11.1: Goodness of Fit Notation
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Chapter 9: Inferences from Two Samples
9.3 Two Means, Two Dependent Samples, Matched Pairs
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Chapter 9: Inferences from Two Samples
9.2: Two Means, Independent Samples
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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2. 8.1 Basics of Hypothesis Testing
8.2 Testing a Claim about a Proportion
8.3 Testing a Claim About a Mean
8.4 Testing a Claim About a Standard Deviation or Variance
2
Objectives:
• Understand the definitions used in hypothesis testing.
• State the null and alternative hypotheses.
• State the steps used in hypothesis testing.
• Test proportions, using the z test.
• Test means when is known, using the z test.
• Test means when is unknown, using the t test.
• Test variances or standard deviations, using the chi-square test.
• Test hypotheses, using confidence intervals.
Chapter 8: Hypothesis Testing
3. 1. The traditional method (Critical Value Method) (CV)
2. The P-value method
P-Value Method: In a hypothesis test, the P-value is the probability of getting a value of the
test statistic that is at least as extreme as the test statistic obtained from the sample data,
assuming that the null hypothesis is true.
3. The confidence interval (CI)method
Because a confidence interval estimate of a population parameter contains the likely values of that parameter,
reject a claim that the population parameter has a value that is not included in the confidence interval.
Equivalent Methods: A confidence interval estimate of a proportion might lead to a conclusion different
from that of a hypothesis test.
Recall: 8.1 Basics of Hypothesis Testing: 3 methods used to test hypotheses:
3
Construct a confidence interval with
a confidence level selected:
Significance Level for
Hypothesis Test: α
Two-Tailed Test:
1 – α
One-Tailed
Test: 1 – 2α
0.01 99% 98%
0.05 95% 90%
0.10 90% 80%
A statistical hypothesis is a assumption about a population parameter. This conjecture may or may not be
true. The null hypothesis, symbolized by H0, and the alternative hypothesis, symbolized by H1
4. 4
Type I error: The mistake of rejecting the null hypothesis when it is
actually true. The symbol α (alpha) is used to represent the
probability of a type I error. (A type I error occurs if one rejects the
null hypothesis when it is true.)
The level of significance is the maximum probability of committing
a type I error: α = P(type I error) = P(rejecting H0 when H0 is
true) and Typical significance levels are: 0.10, 0.05, and 0.01
For example, when a = 0.10, there is a 10% chance of rejecting a
true null hypothesis.
Type II error: The mistake of failing to reject the null hypothesis
when it is actually false. The symbol β(beta) is used to represent the
probability of a type II error. (A type II error occurs if one does not
reject the null hypothesis when it is false.) β = P(type II error) =
P(failing to reject H0 when H0 is false)
Procedure for Hypothesis Tests
Step 1 State the null and alternative
hypotheses and identify the claim (H0 , H1).
Step 2 Test Statistic (TS): Compute
the test statistic value that is relevant to
the test and determine its sampling
distribution (such as normal, t, χ²).
Step 3 Critical Value (CV) :
Find the critical value(s) from the appropriate
table.
Step 4 Make the decision to
a. Reject or not reject the null
hypothesis.
b. The claim is true or false
c. Restate this decision: There is / is
not sufficient evidence to support
the claim that…
5. Objective: Conduct a formal hypothesis test of a claim about a population
proportion p.
Recall: 8.2 Testing a Claim about a Proportion
Notation
n = sample size or number of
trials
p = population proportion (used
in the the null hypothesis)
𝑝 =
𝑥
𝑛
= Sample proportion
Requirements
1. The sample observations are a simple random sample.
2. The conditions for a binomial distribution are
satisfied:
• There is a fixed number of trials.
• The trials are independent.
• Each trial has two categories of “success” and “failure.”
• The probability of a success remains the same in all
trials.
3. The conditions np ≥ 5 and nq ≥ 5 are both satisfied, so
the binomial distribution of sample proportions can be
approximated by a normal distribution with
𝜇 = 𝑛𝑝, 𝜎 = 𝑛𝑝𝑞
5
ˆ
p p
z
pq n
TI Calculator:
1 - Proportion Z - test
1. Stat
2. Tests
3. 1 ‒ PropZTest
4. Enter Data or
Stats (p, x, n)
5. Choose RTT, LTT,
or 2TT
TI Calculator:
Confidence Interval:
proportion
1. Stat
2. Tests
3. 1-prop ZINT
4. Enter: x, n & CL
6. Key Concept: Testing a claim about a population mean
Objective: Use a formal hypothesis test to test a claim about a
population mean µ.
1. The population standard deviation σ is not known.
2. The population standard deviation σ is known.
Recall: 8.3 Testing a Claim About a Mean
The z test is a statistical test for the
mean of a population. It can be used
when n 30, or when the population is
normally distributed and is known.
The formula for the z test is (Test
Statistic): 𝑍 =
𝑥−𝜇
𝜎/ 𝑛
where
𝑥 = sample mean
μ = hypothesized population mean
= population standard deviation
n = sample size
The t test is a statistical test for the
mean of a population. It can be
used when n 30, or when the
population is normally distributed
and is not known.
The formula for the t test is
(Test Statistic): 𝑡 =
𝑥−𝜇
𝑠/ 𝑛
where
𝑥 = sample mean
μ = hypothesized population mean
= population standard deviation
n = sample size 6
TI Calculator:
Mean: T ‒ Test
1. Stat
2. Tests
3. T ‒ Test
4. Enter Data or Stats (p, x, n)
5. Choose RTT, LTT, or 2TT
6. Calculate
TI Calculator:
Mean: Z ‒ Test
1. Stat
2. Tests
3. Z ‒ Test
4. Enter Data or Stats (p, x, n)
5. Choose RTT, LTT, or 2TT
6. Calculate
7. Key Concept:
Conduct a formal hypothesis test of a claim made about a population standard
deviation σ or population variance σ².
The chi-square distribution is also used to test a claim about a single variance or standard deviation.
8.4 Testing a Claim About a Standard Deviation or Variance
Notation
n = sample size
d.f. = n – 1
s = sample standard deviation
σ = population standard deviation
s² = sample variance
σ² = population variance
When testing claims about σ or σ²,
the P-value method, the critical
value method, and the confidence
interval method are all equivalent
in the sense that they will always
lead to the same conclusion.
Requirements
1. The sample is a simple
random sample.
2. The population has a normal
distribution. (This is a fairly
strict requirement.)
Test Statistic
7
2
2
2
( 1)n s
8. Properties of the Chi-Square Distribution
1. All values of χ² are nonnegative, and the distribution is not symmetric.
2. There is a different χ² distribution for each number of degrees of freedom.
3. The critical values are found in Chi-Square Table using degrees of freedom = n – 1
An important note if using Chi-Square Table for finding critical values:
In Chi-Square Table, each critical value of χ² in the body of the table corresponds to an area given in the top
row of the table, and each area in that top row is a cumulative area to the right of the critical value.
8.4 Testing a Claim About a Standard Deviation or Variance
8
Assumptions for the χ² Test for a Variance or a Standard Deviation
1. The sample must be randomly selected from the population.
2. The population must be normally distributed for the variable under study.
3. The observations must be independent of one another.
9. 9
a. Find the critical chi-square value for 15 degrees of freedom when α = 0.05 and the test is right-
tailed.
b. Find the critical chi-square value for 10 degrees of freedom when α = 0.05 and the test is left-tailed.
Example 1
2
24.996 2
3.940
left-tailed: 1 – α = 1
– 0.05 = 0.95.
The chi-square table
gives the area to the
right of the CV.
10. 10
Find the critical chi-square value for 22 degrees of freedom when α = 0.05 and a two-tailed test is
conducted.
Example 2
df = 22
Areas 0.025 and 0.975 correspond
to chi-square values of :
𝝌 𝑳
𝟐
= 𝟏𝟎. 𝟗𝟖𝟐, 𝝌 𝑹
𝟐
= 𝟑𝟔. 𝟕𝟖𝟏
11. 11
An instructor wishes to see whether the variation in scores of the 23 students in her class is less than the
variance of the population. The variance of the class is 198. Is there enough evidence to support the
claim that the variation of the students is less than the population variance (2 =225) at α = 0.05?
Assume that the scores are normally distributed.
Example 3
CV: α = 0.05 & df = n − 1
= 22 →CV: χ² = 12.338
H0: 2 = 225 & H1: 2 < 225, claim, LTTSolution: ND,
n = 23, s2 = 198,
2 =225 , α = 0.05
Decision:
a. Do not Reject (Fail to reject) H0
b. The claim is False
c. There is not enough evidence to support the claim that the
variation in test scores of the instructor’s students is less than
the variation in scores of the population.
19.36
2
2
2
( 1)n s
2
2
2
( 1)
:
n s
TS
(23 1)198
225
Step 1: H0 , H1, claim & Tails
Step 2: TS Calculate (TS)
Step 3: CV using α
Step 4: Make the decision to
a. Reject or not H0
b. The claim is true or false
c. Restate this decision: There is /
is not sufficient evidence to
support the claim that…
12. 12
A researcher wishes to test the claim that the variance of the nicotine content
of a cigarette manufacturer is 0.644. Nicotine content is measured in milligrams, and
assume that it is normally distributed. A sample of 20 cigarettes has a standard
deviation of 1.00 milligram. At α = 0.05, test the claim that that the variance of the
nicotine content of its cigarettes is 0.644.
Example 4
CV: α = 0.05 & df = n − 1 = 19 →
CV: The critical values are 32.852 and 8.907
H0: 2 = 0.644 (claim) and H1: 2 0.644, 2TT
Solution: ND, n = 20,
2 = 0.644, s = 1.00,
α = 0.05
Decision:
a. Do not reject H0
b. The claim is True
c. There is sufficient evidence to support the claim
that the variance of the nicotine content of its
cigarettes is 0.644.
2
19(1)
0.644
29.5
2
2
2
( 1)n s
2
2
2
( 1)
:
n s
TS
Step 1: H0 , H1, claim & Tails
Step 2: TS Calculate (TS)
Step 3: CV using α
Step 4: Make the decision to
a. Reject or not H0
b. The claim is true or false
c. Restate this decision: There is /
is not sufficient evidence to
support the claim that…