You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly different from 79% at a level of significance of αα = 0.10. According to your sample,...

You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly different from 79% at a level of significance of αα = 0.10. According to your sample, 86 out of 98 potential voters prefer the Democratic candidate.

1. For this study, we should use


2. The null and alternative hypotheses would be:
    Ho:           (please enter a decimal)
    H₁:           (Please enter a decimal)

1. The test statistic     = (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      the null hypothesis.


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

   
   
   • The data suggest the population proportion is not
     significantlydifferent from 79% at αα = 0.10, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 79%.
   
   
   • The data suggest the populaton proportion is
     significantly
     different from 79% at αα = 0.10, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 79%
   
   
   • The data suggest the population proportion is not
     significantlydifferent from 79% at αα = 0.10, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 79%.
   
   

   
   
   
   


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

   
   
   • There is a 3.34% chance of a Type I error.
   
   
   • If the sample proportion of voters who prefer the Democratic candidate is 88% and if another 98 voters are surveyed then there would be a 3.34% chance that we would conclude either fewer than 79% of all voters prefer the Democratic candidate or more than 79% of all voters prefer the Democratic candidate.
   
   
   • There is a 3.34% chance that the percent of all voters who prefer the Democratic candidate differs from 79%.
   
   
   • If the population proportion of voters who prefer the Democratic candidate is 79% and if another 98 voters are surveyed then there would be a 3.34% chance that either more than 88% of the 98 voters surveyed prefer the Democratic candidate or fewer than 70% of the 98 voters surveyed prefer the Democratic candidate.
   
   

   
   
   
   


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

   
   
   • There is a 10% chance that the earth is flat and we never actually sent a man to the moon.
   
   
   • If the proportion of voters who prefer the Democratic candidate is different from 79% and if another 98 voters are surveyed then there would be a 10% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is equal to 79%.
   
   
   • If the population proportion of voters who prefer the Democratic candidate is 79% and if another 98 voters are surveyed then there would be a 10% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is different from 79%
   
   
   • There is a 10% chance that the proportion of voters who prefer the Democratic candidate is different from 79%.