Question

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.

1. Find the p-value. (Round your answer to four decimal places.)

Answer 1

Let p₁ = The Proportion of Nevadans who are reported being of two or more races = 17/500 = 0.034

Let p₂ = The Proportion of North Dakotans who are reported being of two or more races = 9/1000 = 0.009

Let = Overall proportion = (17+9)/(1000+500) = 0.0173

1 - = 0.9827

   = 0.05 (default level)

(a) The Hypothesis:

H0: p₁ = p₂ : The population percentage for Nevada is equal to the population percentage for North Dakota.

Ha: p₁ > p₂ : The population percentage for Nevada is greater than the population percentage for North Dakota.

This is a Right tailed Test.

The Test Statistic:

The p Value:    The p value (Right tail) for Z = 3, is; p value = 0.0013

The Critical Value: The critical value (Right tail) at = 0.05, Zcritical = 1.28

The Decision Rule: If Zobserved is > Zcritical Then Reject H0.

Also If the P value is < , Then Reject H0

The Decision:    Since Z observed (3.00) is > Zcritical (1.28), We Reject H0.

Also since P value (0.0013) is < (0.05), We Reject H0.

The Conclusion:   There is sufficient evidence at the 95% significance level to conclude that the population percentage for Nevada is statistically higher than the population percentage for North Dakota.