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Lab 1: chi-square goodness-of-fit

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

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

Note

You may need to combine two categories so that each cell has an expected value of at least five.
  1. Record the values.
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
  2. Construct a histogram of the data. Make five to six intervals. Sketch the graph using a ruler and pencil. Scale the axes.
    Blank graph with relative frequency on vertical
  3. Calculate the following:
    1. x ¯ = ________
    2. s = ________
    3. s 2 = ________

Uniform distribution

Test to see if grocery receipts follow the uniform distribution.

  1. Using your lowest and highest values, X ~ U (_______, _______)
  2. Divide the distribution into fifths.
  3. Calculate the following:
    1. lowest value = _________
    2. 20 th percentile = _________
    3. 40 th percentile = _________
    4. 60 th percentile = _________
    5. 80 th percentile = _________
    6. 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
    1 st
    2 nd
    3 rd
    4 th
    5 th
  5. H 0 : ________
  6. H 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 ¯ as the decay parameter, X ~ Exp (_________).
  2. Calculate the following:
    1. lowest value = ________
    2. first quartile = ________
    3. 37 th percentile = ________
    4. median = ________
    5. 63 rd percentile = ________
    6. 3 rd quartile = ________
    7. 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
    1 st
    2 nd
    3 rd
    4 th
    5 th
    6 th
  4. H 0 : ________
  5. H 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

Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
Kate Reply
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Kate Reply
what is the change in momentum of a body?
Eunice Reply
what is a capacitor?
Raymond Reply
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
Maria Reply
please solve
Sharon
8m/s²
Aishat
What is Thermodynamics
Muordit
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
Saheed Reply
50 m/s due south east
Someone
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
Ramon Reply
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
Someone
definitely of physics
Haryormhidey Reply
how many start and codon
Esrael Reply
what is field
Felix Reply
physics, biology and chemistry this is my Field
ALIYU
field is a region of space under the influence of some physical properties
Collete
what is ogarnic chemistry
WISDOM Reply
determine the slope giving that 3y+ 2x-14=0
WISDOM
Another formula for Acceleration
Belty Reply
a=v/t. a=f/m a
IHUMA
innocent
Adah
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
Nassze Reply
how do lnternal energy measures
Esrael
Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.
JALLAH Reply
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you. Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Robert
like charges repel while unlike charges atttact
Raymond
What is specific heat capacity
Destiny Reply
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
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