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.

Explain why you chose the distribution you did for the Exercise 10.56.

Short answer

Our hypothesis test uses the normal distribution for two proportions because our sample sizes are much larger than 5.

Step-by-step solution

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.

Step 2:Explain why you chose the distribution you did for the Exercise 10.56.

The distribution used in the preceding exercise is the Normal distribution. Because the sample size is substantially larger than 5, this distribution was chosen.