Question

Use the following information to answer the next twelve exercises. In the recent Census, three percent of the U.S. population reported being of two or more races. However, the percent varies tremendously from state to state. Suppose that two random surveys are conducted. In the first random survey, out of 1,000 North Dakotans, only nine 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.

In words, define the random variable for this test.

Short answer

The difference in proportions (percentages) of populations of two or more races in Nevada and North Dakota is the random variable for this test.

Step-by-step solution

Given information

Three percent of the population of the United States reported being of two or more races in the most recent census. However, the percentage varies greatly from one state to the next. Assume two surveys are done at random. Only nine persons out of 1,000 North Dakotans claimed being of two or more races in the initial random survey. In the second random survey, 17 persons out of 500 Nevadans said they were of two or more races. Conduct a hypothesis test to see if the population percentages in the two states are the same or if Nevada's percentage is statistically higher than North Dakota's.

Define the random variable for this test in words.

The difference between the proportions (percentages) of the populations in Nevada and North Dakota that are of two or more races is the random variable of interest for this test.

$p_{\text{nevada}}-p_{\text{Northdakota}}$.

Here, $p_{\text{Nevada}}$is the proportion of people reported being of two or more races in Nevada and $p_{\text{Northdakota}}$ is the proportion of people reported being of two or more races in North Dakota.