Here are the steps to solve this problem:
1) State the null and alternative hypotheses:
H0: σ1^2 = σ2^2 (the variances are equal)
Ha: σ1^2 ≠ σ2^2 (the variances are unequal)
2) Specify the significance level: α = 0.05
3) Calculate the F-statistic:
F = (0.0428/120) / (0.0395/80) = 1.0833
4) Find the p-value:
This is a left-tailed test since s1 < s2. From the F-distribution table with degrees of freedom v1 = 80-1
Negative Binomial Distribution introduction & over view under the complementary Statistics syllabus of University of Calicut in BSc core of Mathematics, Physics & Computer Science.
T-distribution is the most famous theoretical probability distribution in continuous family of distributions. T distribution is used in estimation where normal distribution cannot be used to estimate population parameters. Copy the link given below and paste it in new browser window to get more information on T distribution:- http://www.transtutors.com/homework-help/statistics/t-distribution.aspx
Negative Binomial Distribution introduction & over view under the complementary Statistics syllabus of University of Calicut in BSc core of Mathematics, Physics & Computer Science.
T-distribution is the most famous theoretical probability distribution in continuous family of distributions. T distribution is used in estimation where normal distribution cannot be used to estimate population parameters. Copy the link given below and paste it in new browser window to get more information on T distribution:- http://www.transtutors.com/homework-help/statistics/t-distribution.aspx
It is very difficult to distinguish the differences between ANOVA and regression. This is because both terms have more similarities than differences. It can be said that ANOVA and regression are the two sides of the same coin.
Assumptions of parametric and non-parametric tests
Testing the assumption of normality
Commonly used non-parametric tests
Applying tests in SPSS
Advantages of non-parametric tests
Limitations
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Chapter 9: Inferences from Two Samples
9.4: Two Variances or Standard Deviations
TitleABC123 Version X1Practice Set 5QNT275 Version.docxherthalearmont
Title
ABC/123 Version X
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Practice Set 5
QNT/275 Version 6
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University of Phoenix Material
Practice Set 5
Practice Set 5
1. This distribution has only one parameter. The curve is skewed to the right for small df and
becomes symmetric for large df. The entire distribution curve lies to the right of the vertical
axis. The distribution assumes nonnegative values only
A. t distribution
B. Normal distribution
C. Chi-square distribution
D. Linear regression.
2. Find the value of x2 for 12 degrees of freedom and an area of .025 in the right tail of the chi-
square distribution curve. What is the value of chi-square? Round to three decimal places
3. Determine the value of x2 for 14 degrees of freedom and an area of .10 in the left tail of the
chi-square distribution curve. What is the value of chi-square? Round to three decimal places
4. Determine the value of x2 for 23 degrees of freedom and an area of .990 in the left tail of the
chi-square distribution curve. What is the value of chi-square? Round to three decimal places.
5. Α ____________ compares the observed frequencies from a multinomial experiment with
expected frequencies derived from a certain pattern or theoretical distribution. The test
evaluates how well the observed frequencies fit the expected frequencies.
A. Goodness-of-fit test
B. Chi-square test
C. Linear regression
6. The __________ are the frequencies obtained from the performance of a
multinomial experiment. The expected frequencies are the frequencies that we expect to obtain
if the null hypothesis is true.
A. Observed frequencies
B. Expected frequencies
C. Fluctuating frequencies
7. The expected frequency of a category is given by Ε = np where n is the sample size and p is the
probability that an element belongs to that category if the null hypothesis is true. The
________ for a goodness–of–fit test are k – 1, where k denotes the number of possible
outcomes (or categories) for the experiment.
A. Number of observations
B. Degrees of freedom
C. Total population
8. This model includes only two variables, one independent and one dependent, is called a _____1______. The ___2____ is the one being explained, and the ___3___ is the one used to explain the variation in the dependent variable. Select the correct letter that would make the sentence true.
1. Select a letter from the list to make this statement true.
2. Select a letter from the list to make this statement true.
3. Select a letter from the list to make this statement true.
A. Linear model
B. Qualitative variable
C. Multivariate analysis of variance
D. Independent variable
E. Simple regression model
F. One-way Analysis of Variance
G. Dependent variable
H. Quantitative variable
9. A population data set produced the following information.
N=460, ∑x=3920, ∑y=2650, ∑xy=26,570, ∑x2=48,530
Find the population regression line. R ...
A chi-squared test is a statistical hypothesis test that is valid to perform when the test statistic is chi-squared distributed under the null hypothesis, specifically Pearson's chi-squared test and variants
differences between the observed values
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
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
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
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.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
2. F- Distribution
Theoretically, we might define the F distribution to
be the ratio of two independent chi-square distributions,
each divided by their degrees of freedom. Hence, if f is a
value of the random variable F, we have:
F= = =
Where X12 is a value of a chi-square distribution with v1= n1-1 degrees
of freedom and X22 is a value of a chi-square distribution with v2= n2-1
degrees of freedom. We say that f is a value of the F- distribution with
v1 and v2 degrees of freedom.
3. To obtain an f value, first select a random sample of size n1 from a normal
Population having a variance and compute .
An independent sample of size n, is then selected from a second
normal population with variance and is computed.
The ratio of the two quantities
and is the denominator is called the F- distribution, with v1 and
v2 degrees of freedom.
4. • The number of degrees of freedom associated
with the sample variance in the numerator is
always stated first, followed by the number of
degrees of freedom associated with the
sample variance in the denominator. Thus the
curve of the F distribution depends not only
on the two parameters v1 and v2 but also on
the order in which we state them. Once
these two values are given, we can identify
the curve.
5. 6 and 24 degrees of freedom
6 and 10 degrees of freedom
TYPICAL
F DISTRIBUTION
6. • Let be the f value above which we find an
area equal to . This is illustrated by the
shaded region.
• Example: The f value with 6 and 10 degrees of
freedom, leaving an area of 0.05 to the right,
is = 3.22. By means of the following
theorem, Table A.7 can be used to find values
of and .
8. • Writing for with v1 and v2 degrees
of freedom. THEN,
Thus the f value with 6 and 10 degrees of freedom, leaving an area of 0.95
to the right, is
=
10. • The F distribution is applied primarily in the
analysis of variance where we wish to test the
equality of several means simultaneously. We
shall use the F distribution to make inferences
concerning the variance of two normal
populations.
12. FORMULA:
Where :
is the greater variance
is the smaller variance
13. • Example 9.1.31.
A group of Mass Communication students
study telephone calls at the registrar’s office.
The students monitor the time of the
incoming and outgoing calls for one day. They
that 17 incoming calls last an average of 4.13
minutes with a variance of 1.36 test the
hypothesis that the variances of the samples
are equal. Use the 0.05 level of significance.
14. • Solution: We follow the steps in hypothesis
testing.
a. H0 : The variances of the samples are equal.
b. Ha : The variances of the samples are not
equal
15. c. Set
d. Tabular value of F. Use F-test (test about two
variances or standard deviations)
v = (17-1, 12-1)
e. Computed value of F
16. f. Conclusion: Since , accept H0. Hence,
the variances of the samples are equal.
17. Here’s the Solution:
a. H0 : The two samples come from the
population with equal variances.
b. Ha : The two samples come from the
population with smaller variances
18. SEATWORK:
From sample of 25 observations, the
estimate of the standards, the estimate of the
variance of the population was found to 15.0
From another sample of 14 observations, the
estimate variance was found to be 9.7 Can we
accept the hypothesis that the two samples
come from populations with equal variance,
or must we conclude that the variance of the
second population is smaller? Use the 0.01
level of significance.
19.
20. c. Set
d. Tabular value of F. Use F-test.
v = (25-1, 14-1)
e. Computed value of F
f. Conclusion: Since , accept H0. Hence,
the two samples come from the population
with equal variances.
22. QUIZ
Samples from two makers of ball bearings are collected,
and their diameters (in inches) are measured, with the
following results:
•Acme: n1=80, s1=0.0395
•Bigelow: n2=120, s2=0.0428
Assuming that the diameters of the bearings from both
companies are normally distributed, test the claim that there is
no difference in the variation of the diameters between the two
companies.
24. • The hypotheses are:
H0:
Ha :
• α=0.05.
• The test statistic is F test
• Use formula: =
• Since the first sample had the smaller standard
deviation, this is a left-tailed test. The p-value is
• Since > , we fail to reject H0 .
• There is insufficient evidence to conclude that the
diameters of the ball bearings in the two companies
have different standard deviations.