Question

You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly smaller than 73% at a level of significance of αα = 0.05. According to your sample, 49 out of 72 potential voters prefer the Democratic candidate.

1. For this study, we should use Select an answer t-test for a population mean z-test for a population proportion
2. The null and alternative hypotheses would be:
   Ho: ? p μ  ? < > = ≠   (please enter a decimal)   
   H₁: ? μ p  ? ≠ < = >   (Please enter a decimal)

3. The test statistic ? t z  =  (please show your answer to 3 decimal places.)
4. The p-value =  (Please show your answer to 4 decimal places.)
5. The p-value is ? ≤ >  αα
6. Based on this, we should Select an answer accept reject fail to reject  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest the populaton proportion is significantly smaller than 73% at αα = 0.05, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller than 73%
   • The data suggest the population proportion is not significantly smaller than 73% at αα = 0.05, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller than 73%.
   • The data suggest the population proportion is not significantly smaller than 73% at αα = 0.05, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 73%.
8. Interpret the p-value in the context of the study.
   • There is a 73% chance of a Type I error.
   • If the sample proportion of voters who prefer the Democratic candidate is 68% and if another 72 voters are surveyed then there would be a 17.23% chance of concluding that fewer than 73% of all voters surveyed prefer the Democratic candidate.
   • There is a 17.23% chance that fewer than 73% of all voters prefer the Democratic candidate.
   • If the population proportion of voters who prefer the Democratic candidate is 73% and if another 72 voters are surveyed then there would be a 17.23% chance fewer than 68% of the 72 voters surveyed prefer the Democratic candidate.
9. Interpret the level of significance in the context of the study.
   • There is a 5% chance that the proportion of voters who prefer the Democratic candidate is smaller than 73%.
   • If the population proportion of voters who prefer the Democratic candidate is 73% and if another 72 voters are surveyed then there would be a 5% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is smaller than 73%
   • There is a 5% 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 smaller than 73% and if another 72 voters are surveyed then there would be a 5% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is equal to 73%.

Answer 1