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This module provides a practice of Two Population Means and Two Population Proportions 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 two proportions.

Given

In the recent Census, 3 percent of the U.S. population reported being two or more races. However, the percent varies tremendously from state to state. ( Source: http://www.census.gov/prod/cen2010/briefs/c2010br-02.pdf ) Suppose that two random surveys are conducted. In the first random survey, out of 1000 North Dakotans, only 9 people reported being of two or more races. In the second random survey, out of 500 Nevadans, 17 people reported being of two or more races. Conduct a hypothesis test to determine if the population percents are the same for the two states or if the percent for Nevada is statistically higher than for North Dakota.

Hypothesis testing: two proportions

Is this a test of means or proportions?

Proportions

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State the null and alternative hypotheses.

  • H 0 : size 12{H rSub { size 8{0} } :} {}
  • H a : size 12{H rSub { size 8{a} } :} {}
  • H 0 : PN = PND size 12{H rSub { size 8{O} } : rSub { size 8{ ital "PN"} } = rSub { size 8{ ital "PND"} } } {}
  • H a : PN > PND size 12{H rSub { size 8{a} } : rSub { size 8{ ital "PN"} }>rSub { size 8{ ital "PND"} } } {}
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Is this a right-tailed, left-tailed, or two-tailed test? How do you know?

right-tailed

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What is the Random Variable of interest for this test?

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In words, define the Random Variable for this test.

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Which distribution (Normal or student's-t) would you use for this hypothesis test?

Normal

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Explain why you chose the distribution you did for the above question.

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Calculate the test statistic.

3.50

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Sketch a graph of the situation. Mark the hypothesized difference and the sample difference. Shade the area corresponding to the p size 12{p - {}} {} value.

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Find the p size 12{p - {}} {} value:

0.0002

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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 proportion of Nevadans who are two or more races is higher than the proportion of North Dakotans? Why or why not?

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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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