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Student learning outcomes

  • The student will calculate confidence intervals for proportions.


The Ice Chalet offers dozens of different beginning ice-skating classes. All of the class names are put into a bucket. The 5 P.M., Monday night, ages 8 - 12, beginning ice-skating class was picked. In that class were 64 girls and 16 boys. Suppose that we are interested in the true proportion of girls, ages 8 - 12, in all beginning ice-skating classes at the Ice Chalet. Assume that the children in the selected class is a random sample of the population.

Estimated distribution

What is being counted?

In words, define the Random Variable X size 12{X} {} . X = size 12{X={}} {}

The number of girls, age 8-12, in the beginning ice skating class

Calculate the following:

  • x = size 12{x={}} {}
  • n = size 12{n={}} {}
  • p ' = size 12{p'={}} {}

  • 64
  • 80
  • 0.8

State the estimated distribution of X size 12{X} {} . X ~

B ( 80 , 0.80 )

Define a new Random Variable P ' size 12{P'} {} . What is p ' size 12{p'} {} estimating?


In words, define the Random Variable P ' size 12{P'} {} . P ' = size 12{P'={}} {}

The proportion of girls, age 8-12, in the beginning ice skating class.

State the estimated distribution of P ' size 12{P'} {} . P ' ~

Explaining the confidence interval

Construct a 92% Confidence Interval for the true proportion of girls in the age 8 - 12 beginning ice-skating classes at the Ice Chalet.

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

1 - 0.92 = 0.08

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


Calculate the following:

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

  • 0.72
  • 0.88
  • 0.08

The 92% Confidence Interval is:

(0.72; 0.88)

Fill in the blanks on the graph with the areas, upper and lower limits of the confidence interval, and the sample proportion.

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 p ' size 12{p'} {} and level of confidence, suppose that n were increased to 100. Would the error bound become larger or smaller? How do you know?

Using the same p ' size 12{p'} {} and n = 80 size 12{n="80"} {} , how would the error bound change if the confidence level were increased to 98%? Why?

If you decreased the allowable error bound, why would the minimum sample size increase (keeping the same level of confidence)?

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.
yes that's correct
I think
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
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 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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