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.)
Record the values.
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Construct a histogram of the data. Make 5 - 6 intervals. Sketch the graph using a ruler and pencil. Scale the axes.
Calculate the following:
$\overline{x}=$
$s=$
${s}^{2}=$
Uniform distribution
Test to see if grocery receipts follow the uniform distribution.
Using your lowest and highest values,
$X$ ~
$U\left(\text{\_\_\_\_\_\_\_,\_\_\_\_\_\_\_}\right)$
Divide the distribution above into fifths.
Calculate the following:
Lowest value =
20th percentile =
40th percentile =
60th percentile =
80th percentile =
Highest value =
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
${H}_{o}$ :
${H}_{a}$ :
What distribution should you use for a hypothesis test?
Why did you choose this distribution?
Calculate the test statistic.
Find the p-value.
Sketch a graph of the situation. Label and scale the x-axis. Shade the area corresponding to the
p-value.
State your decision.
State your conclusion in a complete sentence.
Exponential distribution
Test to see if grocery receipts follow the exponential distribution with decay
parameter
$\frac{1}{\overline{x}}$ .
Using
$\frac{1}{\overline{x}}$ as the decay parameter,
$X$ ~
$\text{Exp}\left(\text{\_\_\_\_\_\_\_}\right)$ .
Calculate the following:
Lowest value =
First quartile =
37th percentile =
Median =
63rd percentile =
3rd quartile =
Highest value =
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
${H}_{o}$
${H}_{a}$
What distribution should you use for a hypothesis test?
Why did you choose this distribution?
Calculate the test statistic.
Find the p-value.
Sketch a graph of the situation. Label and scale the x-axis. Shade the area corresponding to the
p-value.
State your decision.
State your conclusion in a complete sentence.
Discussion questions
Did your data fit either distribution? If so, which?
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
can someone help me with some logarithmic and exponential equations.
In this morden time nanotechnology used in many field .
1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc
2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc
3- Atomobile -MEMS, Coating on car etc.
and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change .
maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.