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Student learning outcomes

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


The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. ( (External Link)

Let X = size 12{X={}} {} the age of a Winter Foothill College student

Calculating the confidence interval

x ¯ = size 12{ {overline {x}} ={}} {}


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15=(insert symbol here)


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Define the Random Variable, X , in words.

X =

the mean age of 25 randomly selected Winter Foothill students

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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?


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


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Explaining the confidence interval

Construct a 95% Confidence Interval for the true mean age of Winter Foothill College students.

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


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


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Identify the following specifications:

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

  • 24.52
  • 36.28
  • 5.88

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The 95% Confidence Interval is:__________________

( 24 . 52 , 36 . 28 ) size 12{ \( "24","52","36" "." "28" \) } {}

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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 mean, standard deviation and level of confidence, suppose that n size 12{n} {} were 69 instead of 25. Would the error bound become larger or smaller? How do you know?

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Using the same mean, standard deviation and sample size, how would the error bound change if the confidence level were reduced to 90%? Why?

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Questions & Answers

how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
I'm not sure why it wrote it the other way
I got X =-6
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
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a perfect square v²+2v+_
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algebra 2 Inequalities:If equation 2 = 0 it is an open set?
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or infinite solutions?
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
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Kristine 2*2*2=8
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Differences Between Laspeyres and Paasche Indices
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No. 7x -4y is simplified from 4x + (3y + 3x) -7y
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. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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I start with an easy one. carbon nanotubes woven into a long filament like a string
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Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
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good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
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the Beer law works very well for dilute solutions but fails for very high concentrations. why?
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1 It is estimated that 30% of all drivers have some kind of medical aid in South Africa. What is the probability that in a sample of 10 drivers: 3.1.1 Exactly 4 will have a medical aid. (8) 3.1.2 At least 2 will have a medical aid. (8) 3.1.3 More than 9 will have a medical aid.
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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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