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Inside Collection (Textbook):

Textbook by: Barbara Illowsky, Ph.D., Susan Dean. E-mail the authors

# Practice 1: Hypothesis Testing for Two Proportions

Summary: 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

### Exercise 1

Is this a test of means or proportions?

Proportions

### Exercise 2

State the null and alternative hypotheses.

• a. H0:H0: size 12{H rSub { size 8{0} } :} {}
• b. Ha:Ha: size 12{H rSub { size 8{a} } :} {}

#### Solution

• a. H 0 : PN = PND 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 H a : PN > PND size 12{H rSub { size 8{a} } : rSub { size 8{ ital "PN"} } > rSub { size 8{ ital "PND"} } } {}

### Exercise 3

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

right-tailed

### Exercise 4

What is the Random Variable of interest for this test?

### Exercise 5

In words, define the Random Variable for this test.

### Exercise 6

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

Normal

### Exercise 7

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

### Exercise 8

Calculate the test statistic.

3.50

### Exercise 9

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

### Exercise 10

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

0.0002

### Exercise 11

At a pre-conceived α=0.05α=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):

#### Solution

• a. Reject the null hypothesis

## Discussion Question

### Exercise 12

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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