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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's economic development and growth
Popoola Reply
what do you understand by Ceteris Paribus?
Gabriel Reply
explain the uses of microeconomics
Nikita Reply
uses of microeconomics
Nikita
Adam Smith's definition of economics
Sylvia Reply
what is economic deficit
Amjad
this is a situation whereby a nation's outcome or available resources are not enough to the people thereby causing scarcity
Ariel
prices of Quality demanded is equal to Quality supplied
NABUBOLO Reply
it's quantity demand and quantity supplied that's called equilibrium
Romy
no
NABUBOLO
they deal With prices
NABUBOLO
define the elasticity
NABUBOLO
explain different types of elasticity
NABUBOLO
oops 😬 you are right you talk about quality I tell about quantity
Romy
elasticity is the measurement of the percentage change of one economic variable in response to a change in another
Romy
Cross Elasticity of Demand (XED) Income Elasticity of Demand (YED) Price Elasticity of Supply (PES)
Romy
anything else?
Romy
I need to know everything about theory of consumer behavior
Grace
How does one analyze a market where both demand and supply shift?
Gabriel Reply
That's equilibrium market
Ramon
but an equlibrum can appear twice on the same market... both in Movement along the Demand/supply curve of shift in the Curve
Gabriel
I Mean on the same curve..
Gabriel
how can consumer surplus be calculated
Franklyn
How can we analyze the effect on demand or supply if multiple factors are changing at the same time—say price rises and income falls? 
Gabriel Reply
because of fall of income, less will be demanded and much will be supply as a result of price rises. Rise in price always motivate new supplier to enter into the system. But it only possible in the short run
Kweku
yeah.. I think Ceteris Paribus is applied in this case
Gabriel
that is the law of Demand is Inversely related to the law of Supply... so that mean a positive change in demand may produce a negative return to supply I think.
Gabriel
what are the difference between Wants and Needs
Gabriel Reply
When the price is above the equilibrium, explain how market forces move the market price to equilibrium. Do the same when the price is below the equilibrium.
Gabriel
economic problems
Manishankar
yeah please Explain
Gabriel
I don't know this is my question
Manishankar
no it was a mistake...😂😂 can you explain how Wants and needs differs 😌
Gabriel
wants is what human desire but might not need them, human want are mostly articles of ostentatious while need is what human must get to live e.g inferior goods
Ramon
what's equilibrium price
james
equilibrium prices is a situation whereby the price of goods supplied equates to the demand
Ariel
this whereby the prices of quality demanded is equivalent to quality demanded
NABUBOLO
wants are numerous desire man that man can do without if not purchased e.g. cosmetic while need are desires that you cannot do without e.g. food
Franklyn
equilibrium price is that level of output were quantity demanded is equal to quantity supplied
Arthur
what are the importance of studying economics
Bherla Reply
To know if the country is growing or not through the country's GDP
Ariel
to manage our resources
TOBI
compare base years GDP and the current years GDP
james
To tell whether a country is growing there are many factors to be considered not necessarily only the GDP due to weaknesses of GDP approach
james
What is the law of demand
Yaw Reply
price increase demand decrease...price decrease demand increase
Mujahid
ıf the price increase the demand decrease and if the demand increase the price decrease
MUBARAK
all other things being equal, an increase in demand causes a decrease in supply and vice versa
SETHUAH
yah
Johnson
how is the economy of usa now
Johnson
What is demand
jude Reply
Demand is the quantity of goods and services a consumer is willing and able to purchase at various prices over a given period of time.
Yaw
yea
SETHUAH
Okay congratulations I'll join you guys later .
Aj
yes
MUBARAK
demand is the quantity and quality of goods and services a consumer is willingly and able to purchase at a particular price over a given period of time.
TOBI
calculate elasticity of income exercises
HABANABAKIZE Reply
If potatoes cost Jane $1 per kilogram and she has $5 that could possibly spend on potatoes or other items. If she feels that the first kilogram of potatoes is worth $1.50, the second kilogram is worth$1.14, the third is worth $1.05 and subsequent kilograms are worth $0.30, how many kilograms of potatoes will she purchase? What if she only had $2 to spend?
Susan Reply
cause of poverty in urban
DAVY Reply
QI: (A) Asume the following cost data are for a purely competitive producer: At a product price Of $56. will this firm produce in the short run? Why Why not? If it is preferable to produce, what will be the profit-maximizing Or loss-minimizing Output? Explain. What economic profit or loss will the
Falak Reply
Difference between extinct and extici spicies
Amanpreet Reply
While the American heart association suggests that meditation might be used in conjunction with more traditional treatments as a way to manage hypertension
Beverly 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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