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.

What is the random variable of interest for this test?

Short answer

The random variable of interest in this hypothesis test in symbols is given by,

Subscripts: 1= Nevada, 2= North Dakota ${\mathrm{P}}_1^{\text{'}}-{\mathrm{P}}_2^{\text{'}}$

Step-by-step solution

Given information

As per the most recent census, 3% of the population of the United States identified as being of two or more races. However, the percentage varies greatly between states. Assume you perform two random surveys. Only nine respondents claimed being of two or more races in the initial random survey of 1,000 North Dakotans. In the second random survey, 17 persons out of 500 Nevadans claimed to be of two or more races. Conduct a hypothesis test to see if the population percentages in the two states are equal or if Nevada's percentage is statistically higher than North Dakota's.

Find the random variable of interest for this test

The random variable of interest in this hypothesis test in symbols is :

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

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 to be of two or more races in North Dakota.