Question

A news article that you read stated that 57% of voters prefer the Democratic candidate. You think that the actual percent is different. 151 of the 233 voters that you surveyed said that they prefer the Democratic candidate. What can be concluded at the 0.01 level of significance?

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(?, ≤, >) α
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 57% at αα = 0.01, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different 57%.
• *The data suggest the population proportion is not significantly different 57% at αα = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 57%.
• *The data suggest the populaton proportion is significantly different 57% at αα = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different 57%

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

• *There is a 1.6% chance of a Type I error.
• *If the sample proportion of voters who prefer the Democratic candidate is 65% and if another 233 voters are surveyed then there would be a 1.6% chance that we would conclude either fewer than 57% of all voters prefer the Democratic candidate or more than 57% of all voters prefer the Democratic candidate.
• *If the population proportion of voters who prefer the Democratic candidate is 57% and if another 233 voters are surveyed then there would be a 1.6% chance that either more than 65% of the 233 voters surveyed prefer the Democratic candidate or fewer than 49% of the 233 voters surveyed prefer the Democratic candidate.
• *There is a 1.6% chance that the percent of all voters who prefer the Democratic candidate differs from 57%.

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

• *If the population proportion of voters who prefer the Democratic candidate is 57% and if another 233 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 57%
• *If the proportion of voters who prefer the Democratic candidate is different 57% and if another 233 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 57%.
• *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 57%.

Answer 1