In the recent Census, 3 percent of the US population reported being two or more
ID: 3362550 • Letter: I
Question
In the recent Census, 3 percent of the US population reported being two or more races. The percent variesfrom state to state. Suppose that two random surveys are conducted. In the first out of 100 north Dakotans, only 9 people reported being of two or more races. In the second out of 500 Nevadans 17 perople reported being two or more races Construct 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. DO NOT USE TECHNOLOGY except for calculations - in other words use scientific not graphing calculator
a. In words define the random variable for this test?
b. Which distribution? Why?
c. Calculate the test statistic - show your work
d. sketch a graph of the situation Mark the hypothesized difference and the sample difference. Shade the area corresponding to the p value
e. Find the p value: Show how or explain how you got your p value
f. Decision
State the reason for the decision:
Explanation / Answer
We have to test the percentage of people reported being of two or more races for north Dakotans and Nevadans.
We have given for north dakotans , n1 = 100 and from that 9 pople reported being of two or more races.
so x1 = 9 .
for Nevadans , n2 = 500 and from that 17 pople reported being of two or more races.
so x2 = 17
Here we have to use proportion test , because we have to check percentage for given data.
We have to test the hypothesis 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.
That is Ho : p1^ = p2^
H1 : p1^ < p2^
Where p1^ = 9/100 = 0.09 and p2^ = 17/500 = 0.034
Formula for test statistic is :
p1^ - p2^
Z = -----------------------------------------------------
sqrt { ( p1^*(1-p1^))/n1 + (p2^*(1-p2^))/n2 }
0.09 - 0.034
Z = ---------------------------------------------------------------------- = 1.8827
sqrt { ( 0.09*(1-0.09))/100 + (0.034^*(1-0.034^))/500 }
p value = P( Z < 1.88 ) = 0.9699
So using p value approach , if p value > alpha , then we fail to rejct the null hypothesis .
So, 0.9699 > 0.05 , so we can say that we fail to reject the null hypothesis , that is percetage of Nevadans is same as North Dakota .