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.

State the null and alternative hypotheses.

a.$H_0:$

b. $H_a$:

Short answer

The null and alternative hypotheses.

$$\begin{gathered} H_0:p_{\text{Northdakota}}=p_{\text{Nevada}} \\ {H}_1:p_{\text{Nevada}}>p_{\text{Northdakota}} \end{gathered}$$

Step-by-step solution

Part (a) Step 1: 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.

Part (a) Step 2:  The null and alternative hypotheses should be stated.

The null hypothesis that the population percent's are the same is given below,

$H_0:p_{\text{Northdakota}}=p_{\text{Nevada}}$

Part (b) Step 1: Given information

Three percent of the population of the United States declared themselves to be of two or more races in the most recent census. The percentage, on the other hand, varies greatly from state to state. Assume you perform two separate random surveys. Only nine persons claimed being of two or more races in the first random survey of 1,000 people in North Dakota. Out of 500 Nevadans polled in the second random survey, 17 said they were of two or more races. Perform 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.

Part (b) Step 2:  The null and alternative hypotheses should be stated.

The alternative hypothesis that the percent of Nevada higher than North Dakota is given below, $H_1:p_{\text{Nevadans}}>p_{\text{Northdakota}}$