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Student learning outcomes

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


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

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

the mean number of colors of 39 flags

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

μ size 12{μ} {}

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


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"} } } {}

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={}} {}


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


Calculate the following:

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

  • 2.93
  • 3.59
  • 0.33

The 95% Confidence Interval is:

2.93; 3.59

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.

In one complete sentence, explain what the interval means.

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?

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?

Questions & Answers

what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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.
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
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
characteristics of micro business
for teaching engĺish at school how nano technology help us
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
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
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.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Elementary statistics. OpenStax CNX. Dec 30, 2013 Download for free at http://cnx.org/content/col10966/1.4
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