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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
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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?


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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={}} {}


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


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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

find the 15th term of the geometric sequince whose first is 18 and last term of 387
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I'm not sure why it wrote it the other way
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The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
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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
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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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Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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