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Suppose that a committee is studying whether or not there is waste of time in our judicial system. It is interested in the mean amount of time individuals waste at the courthouse waiting to be called for service. The committee randomly surveyed 81 people. The sample mean was 8 hours with a sample standard deviation of 4 hours.

    • 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 time wasted.
    • State the confidence interval.
    • Sketch the graph.
    • Calculate the error bound.
  • Explain in a complete sentence what the confidence interval means.

    • 8
    • 4
    • 81
    • 80
  • t 80 size 12{t rSub { size 8{"80"} } } {}
    • CI: (7.12, 8.88)
    • EB = 0.88

Suppose that an accounting firm does a study to determine the time needed to complete one person’s tax forms. It randomly surveys 100 people. The sample mean is 23.6 hours. There is a known standard deviation of 7.0 hours. The population distribution is assumed to be normal.

    • 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 time to complete the tax forms.
    • State the confidence interval.
    • Sketch the graph.
    • Calculate the error bound.
  • If the firm wished to increase its level of confidence and keep the error bound the same by taking another survey, what changes should it make?
  • If the firm did another survey, kept the error bound the same, and only surveyed 49 people, what would happen to the level of confidence? Why?
  • Suppose that the firm decided that it needed to be at least 96% confident of the population mean length of time to within 1 hour. How would the number of people the firm surveys change? Why?

A sample of 16 small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. The weight of each bag was then recorded. The mean weight was 2 ounces with a standard deviation of 0.12 ounces. The population standard deviation is known to be 0.1 ounce.

    • 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 Variable X size 12{X} {} , in words.
  • Define the Random Variable 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 weight of the candies.
    • State the confidence interval.
    • Sketch the graph.
    • Calculate the error bound.
  • Construct a 98% confidence interval for the population mean weight of the candies.
    • State the confidence interval.
    • Sketch the graph.
    • Calculate the error bound.
  • In complete sentences, explain why the confidence interval in (f) is larger than the confidence interval in (e).
  • In complete sentences, give an interpretation of what the interval in (f) means.

    • 2
    • 0.1
    • 0.12
    • 16
    • 15
  • the weight of 1 small bag of candies
  • the mean weight of 16 small bags of candies
  • N ( 2, 0 . 1 16 ) size 12{ \( 2, { { size 8{0 "." 1} } over { size 8{ sqrt {"16"} } } } \) } {}
    • CI: (1.96, 2.04)
    • EB = 0.04
    • CI: (1.94, 2.06)
    • EB = 0.06

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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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