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A camp director is interested in the mean number of letters each child sends during his/her camp session. The population standard deviation is known to be 2.5. A survey of 20 campers is taken. The mean from the sample is 7.9 with a sample standard deviation of 2.8.

    • x ¯ = size 12{ {overline {x}} ={}} {} ________
    • σ = size 12{σ} {} ________
    • s x = size 12{s rSub { size 8{x} } ={}} {} ________
    • n = size 12{n} {} ________
    • n 1 = size 12{n - 1} {} ________
  • Define the Random Variables X size 12{X} {} and X ¯ size 12{ {overline {X}} } {} , in words.
  • Which distribution should you use for this problem? Explain your choice.
  • Construct a 90% confidence interval for the population mean number of letters campers send home.
    • State the confidence interval.
    • Sketch the graph.
    • Calculate the error bound.
  • What will happen to the error bound and confidence interval if 500 campers are surveyed? Why?

    • 7.9
    • 2.5
    • 2.8
    • 20
    • 19
  • N ( 7 . 9, 2 . 5 20 ) size 12{N \( 7 "." 9, { { size 8{2 "." 5} } over { size 8{ sqrt {"20"} } } } \) } {}
    • CI: (6.98, 8.82)
    • EB: 0.92

Stanford University conducted a study of whether running is healthy for men and women over age 50. During the first eight years of the study, 1.5% of the 451 members of the 50-Plus Fitness Association died. We are interested in the proportion of people over 50 who ran and died in the same eight–year period.

  • Define the Random Variables X size 12{X} {} and P ' size 12{P'} {} , in words.
  • Which distribution should you use for this problem? Explain your choice.
  • Construct a 97% confidence interval for the population proportion of people over 50 who ran and died in the same eight–year period.
    • State the confidence interval.
    • Sketch the graph.
    • Calculate the error bound.
  • Explain what a “97% confidence interval” means for this study.

In a recent sample of 84 used cars sales costs, the sample mean was $6425 with a standard deviation of $3156. Assume the underlying distribution is approximately normal.

  • Which distribution should you use for this problem? Explain your choice.
  • Define the Random Variable X ¯ size 12{ {overline {X}} } {} , in words.
  • Construct a 95% confidence interval for the population mean cost of a used car.
    • State the confidence interval.
    • Sketch the graph.
    • Calculate the error bound.
  • Explain what a “95% confidence interval” means for this study.

  • t 83 size 12{t rSub { size 8{"83"} } } {}
  • mean cost of 84 used cars
    • CI: (5740.10, 7109.90)
    • EB = 684.90

A telephone poll of 1000 adult Americans was reported in an issue of Time Magazine . One of the questions asked was “What is the main problem facing the country?” 20% answered “crime”. We are interested in the population proportion of adult Americans who feel that crime is the main problem.

  • Define the Random Variables X size 12{X} {} and P ' size 12{P'} {} , in words.
  • Which distribution should you use for this problem? Explain your choice.
  • Construct a 95% confidence interval for the population proportion of adult Americans who feel that crime is the main problem.
    • State the confidence interval.
    • Sketch the graph.
    • Calculate the error bound.
  • Suppose we want to lower the sampling error. What is one way to accomplish that?
  • The sampling error given by Yankelovich Partners, Inc. (which conducted the poll) is ± 3%. In 1-3 complete sentences, explain what the ± 3% represents.

Refer to the above problem. Another question in the poll was “[How much are] you worried about the quality of education in our schools?” 63% responded “a lot”. We are interested in the population proportion of adult Americans who are worried a lot about the quality of education in our schools.

  1. Define the Random Variables X size 12{X} {} and P ' size 12{P'} {} , in words.
  2. Which distribution should you use for this problem? Explain your choice.
  3. Construct a 95% confidence interval for the population proportion of adult Americans worried a lot about the quality of education in our schools.
    • State the confidence interval.
    • Sketch the graph.
    • Calculate the error bound.
  4. The sampling error given by Yankelovich Partners, Inc. (which conducted the poll) is ± 3%. In 1-3 complete sentences, explain what the ± 3% represents.

  • N ( 0.63 , (0.63)(0.37) 1000 )
    • CI: (0.60, 0.66)
    • EB = 0.03

Six different national brands of chocolate chip cookies were randomly selected at the supermarket. The grams of fat per serving are as follows: 8; 8; 10; 7; 9; 9. Assume the underlying distribution is approximately normal.

  • Calculate a 90% confidence interval for the population mean grams of fat per serving of chocolate chip cookies sold in supermarkets.
    • State the confidence interval.
    • Sketch the graph.
    • Calculate the error bound.
  • If you wanted a smaller error bound while keeping the same level of confidence, what should have been changed in the study before it was done?
  • Go to the store and record the grams of fat per serving of six brands of chocolate chip cookies.
  • Calculate the mean.
  • Is the mean within the interval you calculated in part (a)? Did you expect it to be? Why or why not?

A confidence interval for a proportion is given to be (– 0.22, 0.34). Why doesn’t the lower limit of the confidence interval make practical sense? How should it be changed? Why?

Try these multiple choice questions.

The next three problems refer to the following: According to a Field Poll, 79% of California adults (actual results are 400 out of 506 surveyed) feel that “education and our schools” is one of the top issues facing California. We wish to construct a 90% confidence interval for the true proportion of California adults who feel that education and the schools is one of the top issues facing California. (Source: http://field.com/fieldpollonline/subscribers/)

A point estimate for the true population proportion is:

  • 0.90
  • 1.27
  • 0.79
  • 400

C

A 90% confidence interval for the population proportion is:

  • (0.761, 0.820)
  • (0.125, 0.188)
  • (0.755, 0.826)
  • (0.130, 0.183)

A

The error bound is approximately

  • 1.581
  • 0.791
  • 0.059
  • 0.030

D

The next two problems refer to the following:

A quality control specialist for a restaurant chain takes a random sample of size 12 to check the amount of soda served in the 16 oz. serving size. The sample mean is 13.30 with a sample standard deviation of 1.55. Assume the underlying population is normally distributed.

Find the 95% Confidence Interval for the true population mean for the amount of soda served.

  • (12.42, 14.18)
  • (12.32, 14.29)
  • (12.50, 14.10)
  • Impossible to determine

B

What is the error bound?

  • 0.87
  • 1.98
  • 0.99
  • 1.74

C

What is meant by the term “90% confident” when constructing a confidence interval for a mean?

  • If we took repeated samples, approximately 90% of the samples would produce the same confidence interval.
  • If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the sample mean.
  • If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean.
  • If we took repeated samples, the sample mean would equal the population mean in approximately 90% of the samples.

C

The next two problems refer to the following:

Five hundred and eleven (511) homes in a certain southern California community are randomly surveyed to determine if they meet minimal earthquake preparedness recommendations. One hundred seventy-three (173) of the homes surveyed met the minimum recommendations for earthquake preparedness and 338 did not.

Find the Confidence Interval at the 90% Confidence Level for the true population proportion of southern California community homes meeting at least the minimum recommendations for earthquake preparedness.

  • (0.2975, 0.3796)
  • (0.6270, 6959)
  • (0.3041, 0.3730)
  • (0.6204, 0.7025)

C

The point estimate for the population proportion of homes that do not meet the minimum recommendations for earthquake preparedness is:

  • 0.6614
  • 0.3386
  • 173
  • 338

A

Questions & Answers

what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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 did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Elementary statistics. OpenStax CNX. Dec 30, 2013 Download for free at http://cnx.org/content/col10966/1.4
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