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9.16 Hypothesis testing of single mean and single proportion:

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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.
  • The student will demonstrate their usage of the "Two Column Model" to conduct a hypothesis test of a single mean with unknown population standard deviation.

Given

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. Could the population mean time on death row be different than 15 years. Test at a 5% significance level.

Use the 'Two Column Model" to perform a step by step hypothesis test for the above problem. Examples are included in the book and a form is also available in your course management system.

Hypothesis testing: single mean

Is this a test of means or proportions?

averages

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"} {}

Is this a right-tailed, left-tailed, or two-tailed test?How do you know?

two-tailed

What symbol represents the Random Variable for this test?

X ¯ size 12{ {overline {X}} } {}

In words, define the Random Variable for this test.

the mean time spent on death row for the 75 inmates

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

No

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

Which test should be used? In 1 -2 complete sentences, explain why.

t − size 12{t - {}} {} test

State the distribution to use for the hypothesis test.

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

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.

Find the p-value.

0.0015

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

Discussion question

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

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Source:  OpenStax, Collaborative statistics using spreadsheets. OpenStax CNX. Jan 05, 2016 Download for free at http://legacy.cnx.org/content/col11521/1.23
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