Question

Are Republicans just as likely as Democrats to display the American flag in front of their residence on the Fourth of July? 449 of the 675 Republicans surveyed display the flag on the Fourth of July and 424 of the 714 Democrats surveyed display the flag on the Fourth of July. What can be concluded at the αα = 0.05 level of significance?

For this study, we should use Select an answer

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

t-test for the difference between two dependent population means

t-test for a population mean

1. The null and alternative hypotheses would be:   

H0: Select an answer μ1 p1  ? = ≠ < >  Select an answer p2 μ2    

H1: Select an answer μ1 p1  ? > < = ≠  Select an answer p2 μ2

2. The test statistic ? z t  =  (please show your answer to 2 decimal places.)
3. The p-value =  (Please show your answer to 4 decimal places.)
4. The p-value is ? > ≤  αα
5. Based on this, we should Select an answer fail to reject reject accept  the null hypothesis.
6. Thus, the final conclusion is that ...
   • The results are statistically significant at αα = 0.05, so there is sufficient evidence to conclude that the proportion of the 675 Republicans who displayed the American flag in front of their residence on the Fourth of July is different from the proportion of the 714 Democrats who displayed the American flag in front of their residence on the Fourth of July.
   • The results are statistically significant at αα = 0.05, 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 different from the population proportion of Democrats who display the American flag in front of their residence on the Fourth of July.
   • The results are statistically insignificant at αα = 0.05, 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 different from the population proportion of Democrats who display the American flag in front of their residence on the Fourth of July.
   • The results are statistically insignificant at αα = 0.05, 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.
7. Interpret the p-value in the context of the study.
   • 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 675 Republicans and 714 Democrats are surveyed then there would be a 0.6% chance of concluding that Republicans and Democrats differ by at least 7.1 when it comes to displaying the American flag in front of their residence on the Fourth of July
   • There is a 0.6% chance that Republicans and Democrats differ by at least 7.1% when it comes to displaying 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 675 Republicans and 714 Democrats are surveyed then there would be a 0.6% chance that the percent of the surveyed Republicans and Democrats who display the American flag in front of their residence on the Fourth of July differ by at least 7.1%
   • There is a 0.6% chance of a Type I error.
8. 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 675 Republicans and 714 Democrats are surveyed then there would be a 5% 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 5% 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 675 Republicans and 714 Democrats are surveyed then there would be a 5% 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 different from the population proportion of Democrats who display the American flag in front of their residence on the Fourth of July
   • There is a 5% chance that the American flag will be redesigned with your picture on it to honor you for passing this class.

Answer 1