<< Chapter < Page Chapter >> Page >

If you are using a student's-t distribution for a homework problem below, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

Among various ethnic groups, the standard deviation of heights is known to be approximately 3 inches. We wish to construct a 95% confidence interval for the mean height of male Swedes. 48 male Swedes are surveyed. The sample mean is 71 inches. The sample standard deviation is 2.8 inches.

    • 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 95% confidence interval for the population mean height of male Swedes.
    • State the confidence interval.
    • Sketch the graph.
    • Calculate the error bound.
  • What will happen to the level of confidence obtained if 1000 male Swedes are surveyed instead of 48? Why?

    • 71
    • 3
    • 2.8
    • 48
    • 47
  • N ( 71 , 3 48 ) size 12{ \( "71", { { size 8{3} } over { size 8{ sqrt {"48"} } } } \) } {}
    • CI: (70.15,71.85)
    • EB = 0.85

In six packages of “The Flintstones® Real Fruit Snacks” there were 5 Bam-Bam snack pieces. The total number of snack pieces in the six bags was 68. We wish to calculate a 96% confidence interval for the population proportion of Bam-Bam snack pieces.

  • 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
  • Calculate p ' size 12{p'} {} .
  • Construct a 96% confidence interval for the population proportion of Bam-Bam snack pieces per bag.
    • State the confidence interval.
    • Sketch the graph.
    • Calculate the error bound.
  • Do you think that six packages of fruit snacks yield enough data to give accurate results? Why or why not?

A random survey of enrollment at 35 community colleges across the United States yielded the following figures (source: Microsoft Bookshelf ): 6414; 1550; 2109; 9350; 21828; 4300; 5944; 5722; 2825; 2044; 5481; 5200; 5853; 2750; 10012; 6357; 27000; 9414; 7681; 3200; 17500; 9200; 7380; 18314; 6557; 13713; 17768; 7493; 2771; 2861; 1263; 7285; 28165; 5080; 11622. Assume the underlying population is normal.

    • x ¯ = size 12{ {overline {x}} ={}} {}
    • 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 95% confidence interval for the population mean enrollment at community colleges in the United States.
    • State the confidence interval.
    • Sketch the graph.
    • Calculate the error bound.
  • What will happen to the error bound and confidence interval if 500 community colleges were surveyed? Why?

    • 8629
    • 6944
    • 35
    • 34
  • t 34 size 12{t rSub { size 8{"34"} } } {}
    • CI: (6244, 11,014)
    • EB = 2385
  • It will become smaller

From a stack of IEEE Spectrum magazines, announcements for 84 upcoming engineering conferences were randomly picked. The mean length of the conferences was 3.94 days, with a standard deviation of 1.28 days. Assume the underlying population is normal.

  • 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 95% confidence interval for the population mean length of engineering conferences.
    • State the confidence interval.
    • Sketch the graph.
    • Calculate the error bound.

Questions & Answers

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary statistics. OpenStax CNX. Dec 30, 2013 Download for free at http://cnx.org/content/col10966/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

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

Ask