6.50 How's it going?: The American National Election Studies (ANES) collects data on voter attitudes andintentions as well as demographic information. In this question we will focus on two variables from theANES 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 thingshave pretty seriously gotten off on the wrong trackTo 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 TotalNortheast295483North Central4477121South62131193West3667103Total171329500There are TWO parts to this question. One is a Chi-Squared GOF and one is a Chi-Squared Test forIndependence. Think about the differences between the two tests to determine which one to use on whichpart.a) Region: According to the 2010 Census, 18% of US residents live in the Northeast, 22% live in theNorth Central region, 37% live in the South, and 23% live in the West. Is this sample representative ofthe population distribution of US residents?1. The hypotheses to test whether the sample is representative of the population distribution of USresidents are:ⒸH₂ μ=0H₂POOH: The sample distribution of regions follows the Census distributionH₂: The sample distribution of regions does not follow the Census distributionOH: The sample distribution of regions is uniformH: The sample distribution of regions is not uniformOH: X²=0M₂: x²02. The expected values for each region are:Northeast:North Central:South:West:3. The test statistic for this hypothesis test is x²4. The number of degrees of freedom associated with this test is:5. The p-value associated with this hypothesis test is:O greater than 1O between .01 and .05O less than .01O between .05 and .16. The result of this hypothesis test is:O since the p-value is large, we fail to reject HO since the p-value is small, we fail to reject HoO since the p-value is small, we reject H, and accept the alternativeO since the p-value is large, we reject H, and accept the alternative7. This means that:O The sample distribution and Census distribution are the sameO The data provide significant evidence to suggest that the sample distribution and Censusdistribution are differentO The data do not provide convincing evidence that the sample distribution differs from theCensus distributionO The sample distribution and Census distribution are differentb) Region and direction:

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 follows: Right Direction Wrong Track Total Northeast 29 54 83 44 77 121 North Central South 62 131 193 West 36 67 103 Total 171 329 500 There are TWO parts to this question. One is a Chi-Squared GOF and one is a Chi-Squared Test for Independence. Think about the differences between the two tests to determine which one to use on which part. 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: OH₂ μ = 0 H₂₂:μ*O OH,: The sample distribution of regions follows the Census distribution H₂: The sample distribution of regions does not follow the Census distribution OH: The sample distribution of regions is uniform H: The sample distribution of regions is not uniform OH: X²=0 H₂: x²0 2. The expected values for each region are: Northeast: North Central: South: West: 3. The test statistic for this hypothesis test is x²= 4. The number of degrees of freedom associated with this test is: 5. The p-value associated with this hypothesis test is: O greater than 1 O between .01 and .05 O less than .01 O between .05 and .1 6. The result of this hypothesis test is: O since the p-value is large, we fail to reject H O since the p-value is small, we fail to reject Ho O since the p-value is small, we reject H, and accept the alternative O since the p-value is large, we reject H, and accept the alternative 7. This means that: O The sample distribution and Census distribution are the same O The data provide significant evidence to suggest that the sample distribution and Census distribution are different O The data do not provide convincing evidence that the sample distribution differs from the Census distribution O The sample distribution and Census distribution are different b) Region and direction: