<< Chapter < Page Chapter >> Page >
This lab incorporate both lab 1 and lab 2 with minitab.

Confidence Interval Lab

Name:

Student learning outcomes:

  • The student will calculate the 90% confidence intervals.
  • The student will interpret confidence intervals.
  • The student will examine the effects that changing conditions has on the confidence interval.
  • The student will examine the relationship between the confidence level and the percent of constructed intervals that contain the population average.

Part i

Collect the data

Check the Real Estate section in your local newspaper or website. (Note: many papers only list them

one day per week. Also, we will assume that homes come up for sale randomly.) Record the

sales prices for 36 randomly selected homes recently listed in the county and indicate whether you found them in the paper or on the website. Include the reference.

Complete the table:

Describe the data

1. Compute the following: (include the session window)

x ¯ size 12{ {overline {x}} } {} = s = n =

2. Define the Random Variable X ¯ size 12{ {overline {X}} } {} in words:

3. State the estimated distribution to use. Use both words and symbols.

Find the confidence interval

1. Using Minitab, calculate the 90% confidence interval and determine the error bound. (include in the session window)

a. Confidence Interval:

b. Error Bound:

2. How much area is in both tails (combined)? α =

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

4. Using Minitab, create the graph for the 90% confidence interval created above. (Graph → Prbability Distribution Plot→View Probability) Include the graph with this lab.

5. Some students think that a 90% confidence interval contains 90% of the data. Use the list of data on the first page and count how many of the data values lie within the confidence interval. What percent is this? Is this percent close to 90%? Explain why this percent should or should not be close to 90%.

6. How many house prices would be needed in the sample to ensure that the error was no more than $2000 for the 90% confidence interval?

Describe the confidence interval

1. In two to three complete sentences, explain what a Confidence Interval means (in general), as if you were talking to someone who has not taken statistics.

2. In one to two complete sentences, explain what this Confidence Interval means for this particular study.

Use the data to construct confidence intervals

1. Using the above information, construct a confidence interval for each confidence level given. (include the session window information)

Confidence Level Error Bound Confidence Interval
85%
95%
98%
99%

2. What happens to the EBM as the confidence level increases? Does the width of the confidence interval increase or decrease? Explain why this happens.

Effect of an outlier

Suppose one of the values input incorrectly. Choose one data value and increase the amount by adding two extra zeroes. (include in the session window)

1. Calculate the 90% confidence interval: _____________

2. Calculate the Error Bound: ____________

3. How does the outlier affect the width of the confidence interval? Use complete sentences.

Part ii

Heights of 100 Women (in Inches)

59.4 63.8 61.8 61.3 61.5 62.9 64.3 60.8 57.9 64.0
71.6 62.9 60.6 59.2 64.3 63.1 65.0 65.5 58.5 66.4
69.3 63.0 69.8 64.1 62.9 62.2 64.1 62.3 63.4 61.2
65.0 63.9 60.0 59.3 60.6 58.7 61.1 65.5 69.2 60.4
62.9 68.7 64.9 64.9 63.8 64.7 65.3 64.7 65.9 58.7
66.5 65.5 66.1 62.4 58.8 66.0 64.6 58.8 62.2 66.7
61.7 61.9 66.8 63.5 64.9 60.5 59.2 66.1 60.0 67.5
55.2 69.6 60.6 60.9 65.7 64.7 61.4 64.9 58.1 63.2
67.2 58.7 65.6 63.3 62.5 65.4 62.0 66.9 62.5 56.6
66.5 63.4 63.8 66.3 70.9 60.2 63.5 57.9 62.4 67.7

1. Listed above are the heights of 100 women. These are in the student data file in the lab. Use MiniTab to randomly select 10 data values. (Calc → Random data → data from a column)

2. Calculate the sample mean and sample standard deviation and record our answer below. Assuming that the population standard deviation is known to be 3.3. Construct a 90% confidence interval for your sample of 10 values. Write the confidence interval you obtained below.

3. Repeat #1 and #2 nine more times, and record the 90% confidence interval for each of your samples. (Note: since you are randomly selecting the 10 data values you may use the same one in more than one sample. Include this portion of your session window)

  • x ¯ size 12{ {overline {x}} } {} = s = CI =
  • x ¯ size 12{ {overline {x}} } {} = s = CI =
  • x ¯ size 12{ {overline {x}} } {} = s = CI =
  • x ¯ size 12{ {overline {x}} } {} = s = CI =
  • x ¯ size 12{ {overline {x}} } {} = s = CI =
  • x ¯ size 12{ {overline {x}} } {} = s = CI =
  • x ¯ size 12{ {overline {x}} } {} = s = CI =
  • x ¯ size 12{ {overline {x}} } {} = s = CI =
  • x ¯ size 12{ {overline {x}} } {} = s = CI =
  • x ¯ size 12{ {overline {x}} } {} = s = CI =

Discussion questions

1. The actual population mean for the 100 heights given above is μ = 63.3. Using the samples above, for how many intervals does the value of μ lie between the endpoints of the confidence interval? .

2. What percentage of the total number of confidence intervals generated contain the mean μ?

3. Is the percent of confidence intervals that contain the population mean 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? Use 2 – 3 complete sentences.

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 in terms a non-statistician would understand.

6. Some students think that a 90% confidence interval contains 90% of the data. Use the first confidence interval calculated and count how many of the 100 data values lie within that confidence interval? What percent is this? Is this percent close to 90%? Using 3 – 4 sentences to explain why it should or should not be close to 90%.

Questions & Answers

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
Daniel
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
Maciej
characteristics of micro business
Abigail
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
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.
Virgil
is Bucky paper clear?
CYNTHIA
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket 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
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
Berger describes sociologists as concerned with
Mueller Reply
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Collaborative statistics (with edits: teegarden). OpenStax CNX. Jul 20, 2009 Download for free at http://legacy.cnx.org/content/col10561/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Collaborative statistics (with edits: teegarden)' conversation and receive update notifications?

Ask