# 10.6 Practice 1: hypothesis testing for two proportions

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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

State the null and alternative hypotheses.

• ${H}_{0}:$
• ${H}_{a}:$
• $\begin{array}{}{H}_{0}{:}_{\text{PN}}{=}_{\text{PND}}\\ \end{array}$
• $\begin{array}{}{H}_{a}{:}_{\text{PN}}{>}_{\text{PND}}\\ \end{array}$

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's-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. Mark the hypothesized difference and the sample difference. Shade the area corresponding to the $p-$ value.

Find the $p-$ value:

0.0002

At a pre-conceived $\alpha =0\text{.}\text{05}$ , 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?

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1 It is estimated that 30% of all drivers have some kind of medical aid in South Africa. What is the probability that in a sample of 10 drivers: 3.1.1 Exactly 4 will have a medical aid. (8) 3.1.2 At least 2 will have a medical aid. (8) 3.1.3 More than 9 will have a medical aid.