Question: Assume that a state has 50% Republicans and 50% Democrats. In a simple random sample of 200 voters in one of the cities in the state there are 110 Democrats and 90 Republicans. Is there a real difference between the voters in the city and voters in the state overall?

1. Identify the appropriate hypothesis test to use and state the null hypothesis. Use a one sample z-test. Null: the observed difference can be explained by chance. The proportions of republicans and democrats is 50%.
2. Conduct the hypothesis test and state your conclusion. Use a significance level of 5% for your test. Percentage of democrats in sample = 55%
   SD box =0.5
   SE sum = 7.07
   Z statistic = 1.41
   P value = 0.079
   Conclusion: Fail to reject the null hypothesis
3. What does the p-value measure? Interpret the p-value you got in part b) above. p-value measures the chance of observing results as we observed or more extreme results, assuming the null hypothesis is true. In this case there’s a 0.929 chance of observing 55% or more democrats.
4. In a larger sample of 500 voters from the same city, there is the same ratio of Democrats to Republicans as in the original sample. Conduct another hypothesis test to determine if there is a real difference between voters in the city and the state based on the new sample. Again, use a 5% level of significance. Do your conclusions change?

SE sum (with new sample size) = 11.18

SE percentage = 2.2

Z statistic = 2

P value = 0.023

Conclusion: Reject null hypothesis

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