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This module provides a practice of Hypothesis Testing of Single Mean and Single Proportion as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.

Student learning outcomes

  • The student will conduct a hypothesis test of a single mean with unknown population standard deviation.


A random survey of 75 death row inmates revealed that the mean length of time on death row is 17.4 years with a standard deviation of 6.3 years. Conduct a hypothesis test to determine if the population mean time on death row could likely be 15 years.

Hypothesis testing: single mean

Is this a test of means or proportions?


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State the null and alternative hypotheses.

  • H o : size 12{H rSub { size 8{O} } :} {}
  • H a : size 12{H rSub { size 8{a} } :} {}
  • H o : μ = 15 size 12{H rSub { size 8{O} } :μ="15"} {}
  • H a : μ 15 size 12{H rSub { size 8{a} } :μ<>"15"} {}
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Is this a right-tailed, left-tailed, or two-tailed test? How do you know?


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What symbol represents the Random Variable for this test?

X ¯ size 12{ {overline {X}} } {}

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In words, define the Random Variable for this test.

the mean time spent on death row for the 75 inmates

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Is the population standard deviation known and, if so, what is it?


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Calculate the following:

  • x ¯ = size 12{ {overline {x}} ={}} {}
  • 6 . 3 = size 12{6 "." 3={}} {}
  • n = size 12{n={}} {}

  • 17.4
  • s size 12{s} {}
  • 75
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Which test should be used? In 1 -2 complete sentences, explain why.

t size 12{t - {}} {} test

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State the distribution to use for the hypothesis test.

t 74 size 12{t rSub { size 8{"74"} } } {}

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Sketch a graph of the situation. Label the horizontal axis. Mark the hypothesized mean and the sample mean, x ¯ size 12{ {overline {x}} } {} . Shade the area corresponding to the p-value.

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Find the p-value.


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At a pre-conceived α = 0 . 05 size 12{α=0 "." "05"} {} , what is your:

  • Decision:
  • Reason for the decision:
  • Conclusion (write out in a complete sentence):

  • Reject the null hypothesis
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Discussion question

Does it appear that the mean time on death row could be 15 years? Why or why not?

Questions & Answers

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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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