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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

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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?

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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

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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.

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Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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