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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

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s. Reply
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are you nano engineer ?
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Mostly, they use nano carbon for electronics and for materials to be strengthened.
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Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
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of graphene you mean?
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Graphene has a hexagonal structure
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I start with an easy one. carbon nanotubes woven into a long filament like a string
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preparation of nanomaterial
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Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
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what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
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silver nanoparticles could handle the job?
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I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
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Source:  OpenStax, Collaborative statistics homework book: custom version modified by r. bloom. OpenStax CNX. Dec 23, 2009 Download for free at http://legacy.cnx.org/content/col10619/1.2
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