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
Is there any normative that regulates the use of silver nanoparticles?
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
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?