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Student learning outcomes

  • The student will calculate confidence intervals for means when the population standard deviation is unknown.

Given

The following real data are the result of a random survey of 39 national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X = size 12{X={}} {} the number of colors on a national flag.

X Freq.
1 1
2 7
3 18
4 7
5 6

Calculating the confidence interval

Calculate the following:

  • x ¯ = size 12{ {overline {x}} ={}} {}
  • s x = size 12{s rSub { size 8{x} } ={}} {}
  • n = size 12{n={}} {}

  • 3.26
  • 1.02
  • 39
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Define the Random Variable, X ¯ size 12{ {overline {X}} } {} , in words. X ¯ = size 12{ {overline {X}} ={}} {} __________________________

the mean number of colors of 39 flags

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What is x ¯ size 12{ {overline {x}} } {} estimating?

μ size 12{μ} {}

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Is σ x size 12{σ rSub { size 8{x} } } {} known?

No

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As a result of your answer to (4), state the exact distribution to use when calculating the Confidence Interval.

t 38 size 12{t rSub { size 8{"38"} } } {}

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Confidence interval for the true mean number

Construct a 95% Confidence Interval for the true mean number of colors on national flags.

How much area is in both tails (combined)? α = size 12{α={}} {}

0.05

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How much area is in each tail? α 2 = size 12{ { {α} over {2} } ={}} {}

0.025

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Calculate the following:

  • lower limit =
  • upper limit =
  • error bound =

  • 2.93
  • 3.59
  • 0.33
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The 95% Confidence Interval is:

2.93; 3.59

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Fill in the blanks on the graph with the areas, upper and lower limits of the Confidence Interval and the sample mean.

Normal distribution curve with two vertical upward lines from the x-axis to the curve. The confidence interval is between these two lines. The residual areas are on either side.

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In one complete sentence, explain what the interval means.

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Discussion questions

Using the same x ¯ size 12{ {overline {x}} } {} , s x size 12{s rSub { size 8{x} } } {} , and level of confidence, suppose that n size 12{n} {} were 69 instead of 39. Would the error bound become larger or smaller? How do you know?

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Using the same x ¯ size 12{ {overline {x}} } {} , s x size 12{s rSub { size 8{x} } } {} , and n = 39 size 12{n="39"} {} , how would the error bound change if the confidence level were reduced to 90%? Why?

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Questions & Answers

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
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 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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