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.

At a pre-conceived α = 0.05, what is your:

a. Decision:

b. Reason for the decision:

c. Conclusion (write out in a complete sentence):

Short answer

(a) Null hypotheses is rejected.

(b) $p-value<\alpha$.

(c) There is sufficient evidence to conclude that the percentage of the population in Nevada who is of two or more races is statistically larger than in North Dakota at the $5\%$significance level.

Step-by-step solution

Part (a) Step 1: Given information

Test at $5\%$level of significance, that is, $\alpha =0.05$

The output form the steps in Exercise 10.28 is given below,

Part (a) Step 2:  Decision

The output leads to the rejection of the null hypothesis, which states that the percentages of two or more races are higher in Nevada than in North Dakota.

Part (b) Step 1: Given information

Test at $5\%$level of significance, that is, $\alpha =0.05$

The output form the steps in Exercise 10.28 is given below,

Part (b) Step 2: Reason for the decision

Since $\alpha >p$-value, reject the null hypothesis.

As a result, Nevada has a higher percentage of people of two or more races than North Dakota.

Part (c) Step 1: Given information

Test at $5\%$level of significance, that is, $\alpha =0.05$

The output form the steps in Exercise 10.28 is given below,

Part (c) Step 2: Simplify

At $5\%$level of significance, there is sufficient data to support the argument that Nevada has a higher percentage of people of two or more races than North Dakota.