Hypothesis Testing: Two Population Means and Two Population Proportions: Practice 1 1.6 2008/06/17 17:50:14 GMT-5 2008/08/15 16:28:45.599 GMT-5 Barbara Illowsky illowskybarbara@deanza.edu Susan Dean deansusan@deanza.edu Connexions cnx@cnx.org elementary statistics 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 explore the properties of hypothesis testing with two proportions.

Given In the 2000 Census, 2.4 percent of the U.S. population reported being two or more races. However, the percent varies tremendously from state to state. (http://www.census.gov/prod/2001pubs/c2kbr01-6.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 Averages Is this a test of averages or proportions? Proportions State the null and alternative hypotheses. a H0: size 12{H rSub { size 8{0} } :} {} b Ha: size 12{H rSub { size 8{a} } :} {} a H 0 : PN = PND size 12{H rSub { size 8{O} } : rSub { size 8{ ital "PN"} } = rSub { size 8{ ital "PND"} } } {} a 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? right-tailed What is the Random Variable of interest for this test? In words, define the Random Variable for this test. Which distribution (Normal or student-t) would you use for this hypothesis test? Normal Explain why you chose the distribution you did for the above question. Calculate the test statistic. 3.50 Sketch a graph of the situation. Label the horizontal axis. 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: 0.0173 At a pre-conceived α=0.05 size 12{α=0 "." "05"} {}, what is your: a Decision: b Reason for the decision: c Conclusion (write out in a complete sentence): aReject 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?