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This module provides homework on Chi-Square Distribution as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.
  • Explain why the “goodness of fit” test and the “test for independence” are generally right tailed tests.
  • If you did a left-tailed test, what would you be testing?

Word problems

For each word problem, use a solution sheet to solve the hypothesis test problem. Go to The Table of Contents 14. Appendix for the chi-square solution sheet. Round expected frequency to two decimal places.

A 6-sided die is rolled 120 times. Fill in the expected frequency column. Then, conduct a hypothesis test to determine if the die is fair. The data below are the result of the 120 rolls.

Face Value Frequency Expected Frequency
1 15
2 29
3 16
4 15
5 30
6 15

The marital status distribution of the U.S. male population, age 15 and older, is as shown below. ( Source: U.S. Census Bureau, Current Population Reports )

Marital Status Percent Expected Frequency
never married 31.3
married 56.1
widowed 2.5
divorced/separated 10.1

Suppose that a random sample of 400 U.S. young adult males, 18 – 24 years old, yielded the following frequency distribution. We are interested in whether this age group of males fits the distribution of the U.S. adult population. Calculate the frequency one would expect when surveying 400 people. Fill in the above table, rounding to two decimal places.

Marital Status Frequency
never married 140
married 238
widowed 2
divorced/separated 20
  • The data fits the distribution
  • The data does not fit the distribution
  • 3
  • 19.27
  • 0.0002
  • Decision: Reject Null; Conclusion: Data does not fit the distribution.

The next two questions refer to the following information . The columns in the chart below contain the Race/Ethnicity of U.S. Public Schools for a recent year, the percentages for the Advanced Placement Examinee Population for that class and the Overall Student Population. ( Source: http://www.collegeboard.com ). Suppose the right column contains the result of a survey of 1000 local students from that year who took an AP Exam.

Race/Ethnicity AP Examinee Population Overall Student Population Survey Frequency
Asian, Asian American or Pacific Islander 10.2% 5.4% 113
Black or African American 8.2% 14.5% 94
Hispanic or Latino 15.5% 15.9% 136
American Indian or Alaska Native 0.6% 1.2% 10
White 59.4% 61.6% 604
Not reported/other 6.1% 1.4% 43

Perform a goodness-of-fit test to determine whether the local results follow the distribution of the U. S. Overall Student Population based on ethnicity.

Perform a goodness-of-fit test to determine whether the local results follow the distribution of U. S. AP Examinee Population, based on ethnicity.

  • 5
  • 13.4
  • 0.0199
  • Decision: Reject null when a = 0 . 05 size 12{a=0 "." "05"} {} ; Conclusion: Local data do not fit the AP Examinee Distribution. Decision: Do not reject null when a = 0 . 01 size 12{a=0 "." "01"} {} ; Conclusion: There is insufficient evidence to conclude that Local data do not fit the AP Examinee Distribution.

The City of South Lake Tahoe, CA, has an Asian population of 1419 people, out of a total population of 23,609 ( Source: U.S. Census Bureau ). Suppose that a survey of 1419 self-reported Asians in Manhattan, NY, area yielded the data in the table below. Conduct a goodness of fit test to determine if the self-reported sub-groups of Asians in the Manhattan area fit that of the Lake Tahoe area.

Race Lake Tahoe Frequency Manhattan Frequency
Asian Indian 131 174
Chinese 118 557
Filipino 1045 518
Japanese 80 54
Korean 12 29
Vietnamese 9 21
Other 24 66

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Collaborative statistics for mt230. OpenStax CNX. Aug 18, 2011 Download for free at http://legacy.cnx.org/content/col11345/1.2
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