<< Chapter < Page Chapter >> Page >

Class Time:

Names:

Student learning outcomes:

  • The student will calculate a 90% confidence interval using the given data.
  • The student will determine the relationship between the confidence level and the percent of constructed intervals that contain the population mean.

Given:

  1. Heights of 100 women (in inches)
    59.4 71.6 69.3 65.0 62.9
    66.5 61.7 55.2 67.5 67.2
    63.8 62.9 63.0 63.9 68.7
    65.5 61.9 69.6 58.7 63.4
    61.8 60.6 69.8 60.0 64.9
    66.1 66.8 60.6 65.6 63.8
    61.3 59.2 64.1 59.3 64.9
    62.4 63.5 60.9 63.3 66.3
    61.5 64.3 62.9 60.6 63.8
    58.8 64.9 65.7 62.5 70.9
    62.9 63.1 62.2 58.7 64.7
    66.0 60.5 64.7 65.4 60.2
    65.0 64.1 61.1 65.3 64.6
    59.2 61.4 62.0 63.5 61.4
    65.5 62.3 65.5 64.7 58.8
    66.1 64.9 66.9 57.9 69.8
    58.5 63.4 69.2 65.9 62.2
    60.0 58.1 62.5 62.4 59.1
    66.4 61.2 60.4 58.7 66.7
    67.5 63.2 56.6 67.7 62.5
    Listed above are the heights of 100 women. Use a random number generator to randomly select 10 data values.
  2. Calculate the sample mean and sample standard deviation. Assume that the population standard deviation is known to be 3.3 inches. With these values, construct a 90% confidence interval for your sample of10 values. Write the confidence interval you obtained in the first space of the table below.
  3. Now write your confidence interval on the board. As others in the class write their confidence intervals on the board, copy them into the table below:
    90% confidence intervals
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________
    __________ __________ __________ __________ __________

Discussion questions

  1. The actual population mean for the 100 heights given above is μ = 63 . 4 size 12{μ="63" "." 4} {} . Using the class listing of confidence intervals, count how many of them contain the population mean μ size 12{μ} {} ; i.e., for how many intervals does the value of μ size 12{μ} {} lie between the endpoints of the confidence interval?
  2. Divide this number by the total number of confidence intervals generated by the class to determine the percent of confidence intervals that contains the mean μ size 12{μ} {} . Write this percent below.
  3. Is the percent of confidence intervals that contain the population mean μ size 12{μ} {} close to 90%?
  4. Suppose we had generated 100 confidence intervals. What do you think would happen to the percent of confidence intervals that contained the population mean?
  5. When we construct a 90% confidence interval, we say that we are 90% confident that the true population mean lies within the confidence interval. Using complete sentences, explain what we mean by this phrase.
  6. Some students think that a 90% confidence interval contains 90% of the data. Use the list of data given (the heights of women) and count how many of the data values lie within the confidence interval that you generated on that page. How many of the 100 data values lie within your confidence interval? What percent is this? Is this percent close to 90%?
  7. Explain why it does not make sense to count data values that lie in a confidence interval. Think about the random variable that is being used in the problem.
  8. Suppose you obtained the heights of 10 women and calculated a confidence interval from this information. Without knowing the population mean μ size 12{μ} {} , would you have any way of knowing for certain if your interval actually contained the value of μ size 12{μ} {} ? Explain.
This lab was designed and contributed by Diane Mathios.

Questions & Answers

find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
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?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
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
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
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
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
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.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
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.
Nerisha Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Collaborative statistics' conversation and receive update notifications?

Ask