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This module provides a lab on Chi-Square Distribution as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.

Class Time:

Names:

Student learning outcome:

  • The student will evaluate data collected to determine if they fit either the uniform or exponential distributions.

Collect the data

You may need to combine two categories so that each cell has an expected value of at least 5.

Go to your local supermarket. Ask 30 people as they leave for the total amount on their grocery receipts. (Or, ask 3 cashiers for the last 10 amounts. Be sure to include the express lane, if it is open.)

  1. Record the values.
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
  2. Construct a histogram of the data. Make 5 - 6 intervals. Sketch the graph using a ruler and pencil. Scale the axes.
    Blank graph with relative frequency on vertical
  3. Calculate the following:
    • x ¯ = size 12{ {overline {x}} } {}
    • s = size 12{s} {}
    • s 2 = size 12{s rSup { size 8{2} } } {}

Uniform distribution

Test to see if grocery receipts follow the uniform distribution.

  1. Using your lowest and highest values, X ~ U _______,_______ size 12{X "~" U left ("_______, _______" right )} {}
  2. Divide the distribution above into fifths.
  3. Calculate the following:
    • Lowest value =
    • 20th percentile =
    • 40th percentile =
    • 60th percentile =
    • 80th percentile =
    • Highest value =
  4. For each fifth, count the observed number of receipts and record it. Then determine the expected number of receipts and record that.
    Fifth Observed Expected
    1st
    2nd
    3rd
    4th
    5th
  5. H o size 12{H rSub { size 8{o} } } {} :
  6. H a size 12{H rSub { size 8{a} } } {} :
  7. What distribution should you use for a hypothesis test?
  8. Why did you choose this distribution?
  9. Calculate the test statistic.
  10. Find the p-value.
  11. Sketch a graph of the situation. Label and scale the x-axis. Shade the area corresponding to the p-value.
    Blank graph with vertical and horizontal axes.
  12. State your decision.
  13. State your conclusion in a complete sentence.

Exponential distribution

Test to see if grocery receipts follow the exponential distribution with decay parameter 1 x .

  1. Using 1 x ¯ size 12{ { {1} over { {overline {x}} } } } {} as the decay parameter, X ~ Exp _______ size 12{X "~" ital "Exp" left ("_______" right )} {} .
  2. Calculate the following:
    • Lowest value =
    • First quartile =
    • 37th percentile =
    • Median =
    • 63rd percentile =
    • 3rd quartile =
    • Highest value =
  3. For each cell, count the observed number of receipts and record it. Then determine the expected number of receipts and record that.
    Cell Observed Expected
    1st
    2nd
    3rd
    4th
    5th
    6th
  4. H o size 12{H rSub { size 8{o} } } {}
  5. H a size 12{H rSub { size 8{a} } } {}
  6. What distribution should you use for a hypothesis test?
  7. Why did you choose this distribution?
  8. Calculate the test statistic.
  9. Find the p-value.
  10. Sketch a graph of the situation. Label and scale the x-axis. Shade the area corresponding to the p-value.
    Blank graph with vertical and horizontal axes.
  11. State your decision.
  12. State your conclusion in a complete sentence.

Discussion questions

  1. Did your data fit either distribution? If so, which?
  2. In general, do you think it’s likely that data could fit more than one distribution? In complete sentences, explain why or why not.

Questions & Answers

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
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
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
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
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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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