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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.


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?


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"} } } {}

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


What is the Random Variable of interest for this test?

In words, define the Random Variable for this test.

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


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

Calculate the test statistic.


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.

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


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

Questions & Answers

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Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
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. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Collaborative statistics (mt230 - fall 2014). OpenStax CNX. Aug 16, 2014 Download for free at http://legacy.cnx.org/content/col11403/1.7
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