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Class Time:

Names:

Student learning outcomes:

  • The student will demonstrate and compare properties of the Central Limit Theorem.

Given:

X = length of time (in days) that a cookie recipe lasted at the Olmstead Homestead. (Assume that each of the different recipes makes the same quantity of cookies.)

Recipe # X size 12{X} {} Recipe # X size 12{X} {} Recipe # X size 12{X} {} Recipe # X size 12{X} {}
1 1 16 2 31 3 46 2
2 5 17 2 32 4 47 2
3 2 18 4 33 5 48 11
4 5 19 6 34 6 49 5
5 6 20 1 35 6 50 5
6 1 21 6 36 1 51 4
7 2 22 5 37 1 52 6
8 6 23 2 38 2 53 5
9 5 24 5 39 1 54 1
10 2 25 1 40 6 55 1
11 5 26 6 41 1 56 2
12 1 27 4 42 6 57 4
13 1 28 1 43 2 58 3
14 3 29 6 44 6 59 6
15 2 30 2 45 2 60 5

Calculate the following:

  • μ x =
  • σ x =

Collect the data

Use a random number generator to randomly select 4 samples of size n = 5 from the given population. Record your samples below. Then, for each sample, calculate the mean to the nearesttenth. Record them in the spaces provided. Record the sample means for the rest of the class.

  1. Complete the table:
    Sample 1 Sample 2 Sample 3 Sample 4 Sample means from other groups:
    Means: x ¯ = size 12{ {overline {x}} ={}} {} x ¯ = size 12{ {overline {x}} ={}} {} x ¯ = size 12{ {overline {x}} ={}} {} x ¯ = size 12{ {overline {x}} ={}} {}
  2. Calculate the following:
    • x ¯ = size 12{ {overline {x}} ={}} {}
    • s x ¯ = size 12{s rSub { size 8{ {overline {x}} } } ={}} {}
  3. Again, use a random number generator to randomly select 4 samples from the population. This time, make the samples of size n = 10 size 12{n="10"} {} . Record the samples below. As before, for each sample, calculate the mean to the nearest tenth. Record them in the spaces provided. Record the sample means for the rest of the class.
    Sample 1 Sample 2 Sample 3 Sample 4 Sample means from other groups:
    Means: x ¯ = size 12{ {overline {x}} ={}} {} x ¯ = size 12{ {overline {x}} ={}} {} x ¯ = size 12{ {overline {x}} ={}} {} x ¯ = size 12{ {overline {x}} ={}} {}
  4. Calculate the following:
    • x ¯ = size 12{ {overline {x}} ={}} {}
    • s x ¯ = size 12{s rSub { size 8{ {overline {x}} } } ={}} {}
  5. For the original population, construct a histogram. Make intervals with bar width = 1 day. Sketch the graph using a ruler and pencil. Scale the axes.
    Blank graph with frequency on the vertical axis and time in days on the horizontal axis.
  6. Draw a smooth curve through the tops of the bars of the histogram. Use 1 – 2 complete sentences to describe the general shape of the curve.

Repeat the procedure for n=5

  1. For the sample of n = 5 days averaged together, construct a histogram of the averages (your means together with the means of the other groups). Make intervals with bar widths = 1 2 day . Sketch the graph using a ruler and pencil. Scale the axes.
    Blank graph with frequency on the vertical axis and time in days on the horizontal axis.
  2. Draw a smooth curve through the tops of the bars of the histogram. Use 1 – 2 complete sentences to describe the general shape of the curve.

Repeat the procedure for n=10

  1. For the sample of n = 10 days averaged together, construct a histogram of the averages (your means together with the means of the other groups). Make intervals with bar widths = 1 2 day . Sketch the graph using a ruler and pencil. Scale the axes.
    Blank graph with frequency on the vertical axis and time in days on the horizontal axis.
  2. Draw a smooth curve through the tops of the bars of the histogram. Use 1 – 2 complete sentences to describe the general shape of the curve.

Discussion questions

  1. Compare the three histograms you have made, the one for the population and the two for the sample means. In three to five sentences, describe the similarities and differences.
  2. State the theoretical (according to the CLT) distributions for the sample means.
    • n = 5 : X ~
    • n = 10 : X ~
  3. Are the sample means for n = 5 and n = 10 “close” to the theoretical mean, μ x ? Explain why or why not.
  4. Which of the two distributions of sample means has the smaller standard deviation? Why?
  5. As n changed, why did the shape of the distribution of the data change? Use 1 – 2 complete sentences to explain what happened.
This lab was designed and contributed by Carol Olmstead.

Questions & Answers

How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
what is Nano technology ?
Bob Reply
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?
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
How can I make nanorobot?
Lily
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
how can I make nanorobot?
Lily
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
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. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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