Question

You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly different from 68% at a level of significance of αα = 0.01. According to your sample, 43 out of 56 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 ( z, t) =_____ (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 (?, >,≤) α
6. Based on this, we should Select an answer (reject, fail to reject, accept) the null hypothesis.
7. Thus, the final conclusion is that ...

*The data suggest the population proportion is not significantly different from 68% 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 68%.

*The data suggest the populaton proportion is significantly different from 68% at αα = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 68%.

*The data suggest the population proportion is not significantly different from 68% at αα = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 68%.

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

• *If the population proportion of voters who prefer the Democratic candidate is 68% and if another 56 voters are surveyed then there would be a 15.88% chance that either more than 76% of the 56 voters surveyed prefer the Democratic candidate or fewer than 60% of the 56 voters surveyed prefer the Democratic candidate.
• *There is a 15.88% chance of a Type I error.
• *If the sample proportion of voters who prefer the Democratic candidate is 76% and if another 56 voters are surveyed then there would be a 15.88% chance that we would conclude either fewer than 68% of all voters prefer the Democratic candidate or more than 68% of all voters prefer the Democratic candidate.
• *There is a 15.88% chance that the percent of all voters who prefer the Democratic candidate differs from 68%.

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

• *If the population proportion of voters who prefer the Democratic candidate is 68% and if another 56 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 68%
• *If the proportion of voters who prefer the Democratic candidate is different from 68% and if another 56 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 68%.
• *There is a 1% chance that the earth is flat and we never actually sent a man to the moon.
• *There is a 1% chance that the proportion of voters who prefer the Democratic candidate is different from 68%.

Answer 1