Are Republicans more likely than Democrats to display the American flag in front of their residence on the Fourth of July? 448 of the 679 Republicans surveyed display the flag on the Fourth of July...

Are Republicans more likely than Democrats to display the American flag in front of their residence on the Fourth of July? 448 of the 679 Republicans surveyed display the flag on the Fourth of July and 479 of the 776 Democrats surveyed display the flag on the Fourth of July. What can be concluded at the αα = 0.10 level of significance?

For this study, we should use Select an answer t-test for a population mean t-test for the difference between two dependent population means t-test for the difference between two independent population means z-test for the difference between two population proportions z-test for a population proportion

1. The null and alternative hypotheses would be:

 H0:H0:  Select an answer μ1 p1  Select an answer < ≠ = >  Select an answer p2 μ2  (please enter a decimal)

 H1:H1:  Select an answer p1 μ1  Select an answer ≠ < = >  Select an answer μ2 p2  (Please enter a decimal)

1. The test statistic ? t z  =  (please show your answer to 3 decimal places.)


2. The p-value =  (Please show your answer to 4 decimal places.)


3. The p-value is ? ≤ >  αα


4. Based on this, we should Select an answer accept fail to reject reject  the null hypothesis.


5. Thus, the final conclusion is that ...
   
   
   

   
   
   • The results are statistically insignificant at αα = 0.10, so there is insufficient evidence to conclude that the population proportion of Republicans who display the American flag in front of their residence on the Fourth of July is greater than the population proportion of Democrats who display the American flag in front of their residence on the Fourth of July.
   
   
   • The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the proportion of the 679 Republicans who displayed the American flag in front of their residence on the Fourth of July is greater than the proportion of the 776 Democrats who displayed the American flag in front of their residence on the Fourth of July.
   
   
   • The results are statistically insignificant at αα = 0.10, so we can conclude that the population proportion of Republicans who display the American flag in front of their residence on the Fourth of July is equal to the population proportion of Democrats who display the American flag in front of their residence on the Fourth of July.
   
   
   • The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the population proportion of Republicans who display the American flag in front of their residence on the Fourth of July is greater than the population proportion of Democrats who display the American flag in front of their residence on the Fourth of July.
   
   

   
   
   
   


6. Interpret the p-value in the context of the study.
   
   
   

   
   
   • If the percent of all Republicans who display the American flag in front of their residence on the Fourth of July is the same as the percent of all Democrats who display the American flag in front of their residence on the Fourth of July and if another 679 Republicans and 776 Democrats are surveyed then there would be a 4.62% chance that the percent of the surveyed Republicans who display the American flag in front of their residence on the Fourth of July would be at least 4.3% more than the percent of the surveyed Democrats who display the American flag in front of their residence on the Fourth of July.
   
   
   • If the sample proportion of Republicans who display the American flag in front of their residence on the Fourth of July is the same as the sample proportion of Democrats who display the American flag in front of their residence on the Fourth of July and if another another 679 Republicans and 776 Democrats are surveyed then there would be a 4.62% chance of concluding that Republicans are at least 4.3% more likely to display the American flag in front of their residence on the Fourth of July
   
   
   • There is a 4.62% chance that Republicans are at least 4.3% more likely to display the American flag in front of their residence on the Fourth of July.
   
   
   • There is a 4.62% chance of a Type I error.
   
   

   
   
   
   


7. Interpret the level of significance in the context of the study.
   
   
   

   
   
   • If the percent of all Republicans who display the American flag in front of their residence on the Fourth of July is the same as the percent of all Democrats who display the American flag in front of their residence on the Fourth of July and if another 679 Republicans and 776 Democrats are surveyed then there would be a 10% chance that we would end up falsely concuding that the population proportion of Republicans who display the American flag in front of their residence on the Fourth of July is greater than the population proportion of Democrats who display the American flag in front of their residence on the Fourth of July
   
   
   • There is a 10% chance that there is a difference in the proportion of Republicans and Democrats who display the American flag in front of their residence on the Fourth of July.
   
   
   • If the percent of all Republicans who display the American flag in front of their residence on the Fourth of July is the same as the percent of all Democrats who display the American flag in front of their residence on the Fourth of July and if another 679 Republicans and 776 Democrats are surveyed then there would be a 10% chance that we would end up falsely concuding that the proportion of these surveyed Republicans and Democrats who display the American flag in front of their residence on the Fourth of July differ from each other.
   
   
   • There is a 10% chance that the American flag will be redesigned with your picture on it to honor you for passing this class.