6.50 How's it going?:  The American National Election Studies (ANES) collects data on voter attitudes and intentions as well as demographic information. In this question we will focus on two variables from the ANES dataset (ANES, 2012).

• region (levels: Northeast, North Central, South, and West)
• whether the respondent feels things in this country are generally going in the right direction or things have pretty seriously gotten off on the wrong track

To keep calculations simple we will work with a random sample of 500 respondents from the ANES dataset. The distribution of responses are as folows:

	Right Direction	Wrong Track	Total
Northeast	29	54	83
North Central	44	77	121
South	62	131	193
West	36	67	103
Total	171	329	500

a) Region: According to the 2010 Census, 18% of US residents live in the Northeast, 22% live in the North Central region, 37% live in the South, and 23% live in the West. Is this sample representative of the population distribution of US residents?

1. The hypotheses to test whether the sample is representative of the population distribution of US residents are:
   • H_o: The sample distribution of regions is uniform
     H_a: The sample distribution of regions is not uniform
   • H_o: The sample distribution of regions follows the Census distribution
     H_a: The sample distribution of regions does not follow the Census distribution
   • H_o: Χ² = 0
     H_a: Χ² ≠ 0
   • H_o: μ = 0
     H_a: μ ≠ 0
   
   
2. The expected values for each region are:
   Northeast:
   North Central:
   South:
   West:
   
3. The test statistic for this hypothesis test is Χ²=
   
4. The numnber of degrees of freedom associated with this test is:
   
5. The p-value associated with this hypothesis test is:
   • between .01 and .05
   • greater than .1
   • less than .01
   • between .05 and .1
   
   
6. The result of this hypothesis test is:
   • Since the p-value is large, we fail to reject H_o
   • Since the p-value is small, we fail to reject H_o
   • Since the p-value is large, we reject H_o and accept the alternative
   • Since the p-value is small, we reject H_o and accept the alternative
   
   
7. This means that:
   • The data do not provide convincing evidence that the sample distribution differs from the Census distribution
   • The data provide significant evidence to suggest that the sample distribution and Census distribution are different
   • The sample distribution and Census distribution are the same
   • The sample distribution and Census distribution are different
   
   

b) Region and direction:

1. What are the hypotheses for evaluating whether or not a relationship between region and opinion on direction exists?
   • H_o: Region and direction are independent
     H_a: Region and direction are associated
   • H_o: Χ² = 0
     H_a: Χ² ≠ 0
   • H_o: Region and direction are associated
     H_a: Region and direction are independent
   • H_o: μ = 0
     H_a: μ ≠ 0
   
   
2. The test statistic for this hypothesis test is: Χ² =
   
3. The number of degrees of freedom associated with this test is:
   
4. The p-value associated with this hypothesis test is:
   • between .05 and .1
   • less than .01
   • greater than .1
   • between .01 and .05
   
   
5. The result of his hypothesis test is:
   • Since the p-value is small, we reject H_o and accept the alternative
   • Since the p-value is small, we fail to reject H_o
   • Since the p-value is large, we fail to reject H_o
   • Since the p-value is large, we reject H_o and accept the alternative
   
   
6. This means that:
   • Region and opinion on direction are independent
   • Region and opionion on direction are associated
   • The data do not provide convincing evidence that region and opinion on direction are associated
   • The data provide significant evidence to suggest that region and opinion on direction are associated