# 11.14 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.
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.
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.

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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?
what king of growth are you checking .?
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What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
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why?
what school?
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biomolecules are e building blocks of every organics and inorganic materials.
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anyone know any internet site where one can find nanotechnology papers?
research.net
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sciencedirect big data base
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Introduction about quantum dots in nanotechnology
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absolutely yes
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for teaching engĺish at school how nano technology help us
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what is the actual application of fullerenes nowadays?
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what is the Synthesis, properties,and applications of carbon nano chemistry
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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
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so some one know about replacing silicon atom with phosphorous in semiconductors device?
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Do you know which machine is used to that process?
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how to fabricate graphene ink ?
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or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
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how did you get the value of 2000N.What calculations are needed to arrive at it
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1 It is estimated that 30% of all drivers have some kind of medical aid in South Africa. What is the probability that in a sample of 10 drivers: 3.1.1 Exactly 4 will have a medical aid. (8) 3.1.2 At least 2 will have a medical aid. (8) 3.1.3 More than 9 will have a medical aid.