# 8.11 Confidence interval lab 4

 Page 1 / 1
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.

## 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)

$\overline{x}$ = s = n =

2. Define the Random Variable $\overline{X}$ 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? $\frac{\alpha }{2}$ =

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 71.6 62.9 60.6 59.2 64.3 63.1 65 65.5 58.5 66.4 69.3 63 69.8 64.1 62.9 62.2 64.1 62.3 63.4 61.2 65 63.9 60 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 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 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 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)

• $\overline{x}$ = s = CI =
• $\overline{x}$ = s = CI =
• $\overline{x}$ = s = CI =
• $\overline{x}$ = s = CI =
• $\overline{x}$ = s = CI =
• $\overline{x}$ = s = CI =
• $\overline{x}$ = s = CI =
• $\overline{x}$ = s = CI =
• $\overline{x}$ = s = CI =
• $\overline{x}$ = 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%.

find the 15th term of the geometric sequince whose first is 18 and last term of 387
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
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
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
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
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.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
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
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.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!