Question

You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly different from 54% at a level of significance of αα = 0.01. According to your sample, 51 out of 100 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: ? p μ  ? ≠ < > =   (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 fail to reject reject accept  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest the population proportion is not significantly different from 54% at αα = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 54%.
   • The data suggest the populaton proportion is significantly different from 54% at αα = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 54%
   • The data suggest the population proportion is not significantly different from 54% at αα = 0.01, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 54%.
8. Interpret the p-value in the context of the study.
   • There is a 54.72% chance that the percent of all voters who prefer the Democratic candidate differs from 54%.
   • There is a 54.72% chance of a Type I error.
   • If the population proportion of voters who prefer the Democratic candidate is 54% and if another 100 voters are surveyed then there would be a 54.72% chance that either fewer than 51% of the 100 voters surveyed prefer the Democratic candidate or more than 57% of the 100 voters surveyed prefer the Democratic candidate.
   • If the sample proportion of voters who prefer the Democratic candidate is 51% and if another 100 voters are surveyed then there would be a 54.72% chance that we would conclude either fewer than 54% of all voters prefer the Democratic candidate or more than 54% of all voters prefer the Democratic candidate.
9. Interpret the level of significance in the context of the study.
   • If the population proportion of voters who prefer the Democratic candidate is 54% and if another 100 voters are surveyed then there would be a 1% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is different from 54%
   • If the proportion of voters who prefer the Democratic candidate is different from 54% and if another 100 voters are surveyed then there would be a 1% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is equal to 54%.
   • There is a 1% chance that the proportion of voters who prefer the Democratic candidate is different from 54%.
   • There is a 1% chance that the earth is flat and we never actually sent a man to the moon.

Answer 1