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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 Recipe # X Recipe # X Recipe # 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:

  1. μ x = _______
  2. σ x = _______

Collect the data

Use a random number generator to randomly select four samples of size n = 5 from the given population. Record your samples in [link] . Then, 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.

  1. Complete the table:
    Sample 1 Sample 2 Sample 3 Sample 4 Sample means from other groups:
    Means: x ¯ = ____ x ¯ = ____ x ¯ = ____ x ¯ = ____
  2. Calculate the following:
    1. x ¯ = _______
    2. s x ¯ = _______
  3. Again, use a random number generator to randomly select four samples from the population. This time, make the samples of size n = 10. Record the samples in [link] . 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 ¯ = ____ x ¯ = ____ x ¯ = ____ x ¯ = ____
  4. Calculate the following:
    1. x ¯ = ______
    2. s x ¯ = ______
  5. For the original population, construct a histogram. Make intervals with a bar width of one day. Sketch the graph using a ruler and pencil. Scale the axes.
    This is a blank graph template. The horizontal axis is labeled Time (days) and the vertical axis is labeled Frequency.
  6. Draw a smooth curve through the tops of the bars of the histogram. Use one to two 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 of 1 2 a day. Sketch the graph using a ruler and pencil. Scale the axes.
    This is a blank graph template. The horizontal axis is labeled Time (days) and the vertical axis is labeled Frequency.
  2. Draw a smooth curve through the tops of the bars of the histogram. Use one to two 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 of 1 2 a day. Sketch the graph using a ruler and pencil. Scale the axes.
    This is a blank graph template. The horizontal axis is labeled Time (days) and the vertical axis is labeled Frequency.
  2. Draw a smooth curve through the tops of the bars of the histogram. Use one to two 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.
    1. n = 5: x ¯ ~ _____(_____,_____)
    2. 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 one to two complete sentences to explain what happened.

Questions & Answers

I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
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
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
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
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Source:  OpenStax, Introduction to statistics i - stat 213 - university of calgary - ver2015revb. OpenStax CNX. Oct 21, 2015 Download for free at http://legacy.cnx.org/content/col11874/1.3
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