# 11.10 Lab 1: chi-square goodness-of-fit

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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.
3. Calculate the following:
• $\overline{x}=$
• $s=$
• ${s}^{2}=$

## Uniform distribution

Test to see if grocery receipts follow the uniform distribution.

1. Using your lowest and highest values, $X$ ~ $U\left(\text{_______,_______}\right)$
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. ${H}_{o}$ :
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.
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 $\frac{1}{\overline{x}}$ .

1. Using $\frac{1}{\overline{x}}$ as the decay parameter, $X$ ~ $\text{Exp}\left(\text{_______}\right)$ .
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. ${H}_{o}$
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.
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

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
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
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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