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Class Time:

Names:

Student learning outcomes:

  • The student will calculate a 90% confidence interval using the given data.
  • The student will determine the relationship between the confidence level and the percent of constructed intervals that contain the population mean.

Given:

  1. Heights of 100 women (in inches)
    59.4 71.6 69.3 65.0 62.9
    66.5 61.7 55.2 67.5 67.2
    63.8 62.9 63.0 63.9 68.7
    65.5 61.9 69.6 58.7 63.4
    61.8 60.6 69.8 60.0 64.9
    66.1 66.8 60.6 65.6 63.8
    61.3 59.2 64.1 59.3 64.9
    62.4 63.5 60.9 63.3 66.3
    61.5 64.3 62.9 60.6 63.8
    58.8 64.9 65.7 62.5 70.9
    62.9 63.1 62.2 58.7 64.7
    66.0 60.5 64.7 65.4 60.2
    65.0 64.1 61.1 65.3 64.6
    59.2 61.4 62.0 63.5 61.4
    65.5 62.3 65.5 64.7 58.8
    66.1 64.9 66.9 57.9 69.8
    58.5 63.4 69.2 65.9 62.2
    60.0 58.1 62.5 62.4 59.1
    66.4 61.2 60.4 58.7 66.7
    67.5 63.2 56.6 67.7 62.5
    Listed above are the heights of 100 women. Use a random number generator to randomly select 10 data values.
  2. Calculate the sample mean and sample standard deviation. Assume that the population standard deviation is known to be 3.3 inches. With these values, construct a 90% confidence interval for your sample of10 values. Write the confidence interval you obtained in the first space of the table below.
  3. Now write your confidence interval on the board. As others in the class write their confidence intervals on the board, copy them into the table below:
    90% confidence intervals
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________

Discussion questions

  1. The actual population mean for the 100 heights given above is μ = 63 . 4 size 12{μ="63" "." 4} {} . Using the class listing of confidence intervals, count how many of them contain the population mean μ size 12{μ} {} ; i.e., for how many intervals does the value of μ size 12{μ} {} lie between the endpoints of the confidence interval?
  2. Divide this number by the total number of confidence intervals generated by the class to determine the percent of confidence intervals that contains the mean μ size 12{μ} {} . Write this percent below.
  3. Is the percent of confidence intervals that contain the population mean μ size 12{μ} {} close to 90%?
  4. Suppose we had generated 100 confidence intervals. What do you think would happen to the percent of confidence intervals that contained the population mean?
  5. When we construct a 90% confidence interval, we say that we are 90% confident that the true population mean lies within the confidence interval. Using complete sentences, explain what we mean by this phrase.
  6. Some students think that a 90% confidence interval contains 90% of the data. Use the list of data given (the heights of women) and count how many of the data values lie within the confidence interval that you generated on that page. How many of the 100 data values lie within your confidence interval? What percent is this? Is this percent close to 90%?
  7. Explain why it does not make sense to count data values that lie in a confidence interval. Think about the random variable that is being used in the problem.
  8. Suppose you obtained the heights of 10 women and calculated a confidence interval from this information. Without knowing the population mean μ size 12{μ} {} , would you have any way of knowing for certain if your interval actually contained the value of μ size 12{μ} {} ? Explain.
This lab was designed and contributed by Diane Mathios.

Questions & Answers

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
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
yes that's correct
Professor
I think
Professor
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
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What is meant by 'nano scale'?
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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
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
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
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
how did you get the value of 2000N.What calculations are needed to arrive at it
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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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