Question

You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly larger than 54% at a level of significance of αα = 0.01. According to your sample, 38 out of 61 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 reject accept fail to reject  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest the population proportion is not significantly larger than 54% at αα = 0.01, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is larger than 54%.
   • The data suggest the populaton proportion is significantly larger than 54% at αα = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is larger than 54%
   • The data suggest the population proportion is not significantly larger than 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%.
8. Interpret the p-value in the context of the study.
   • There is a 9.68% chance that more than 54% of all voters prefer the Democratic candidate.
   • If the sample proportion of voters who prefer the Democratic candidate is 62% and if another 61 voters are surveyed then there would be a 9.68% chance of concluding that more than 54% of all voters surveyed prefer the Democratic candidate.
   • There is a 9.68% chance of a Type I error.
   • If the population proportion of voters who prefer the Democratic candidate is 54% and if another 61 voters are surveyed then there would be a 9.68% chance that more than 62% of the 61 voters surveyed prefer the Democratic candidate.
9. Interpret the level of significance in the context of the study.
   • If the proportion of voters who prefer the Democratic candidate is larger than 54% and if another 61 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%.
   • If the population proportion of voters who prefer the Democratic candidate is 54% and if another 61 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 larger than 54%
   • 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 larger than 54%.

Answer 1

Solution:

a. For this study, we should use

Answer: z-test for a population proportion

b. The null and alternative hypotheses would be:

Answer:

c. The test statistic?

Answer:

  

d. The p-value is

e. The p-value is >

f. Based on this, we should

Answer: Fail to reject the null hypothesis

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

Answer: The data suggest the population proportion is not significantly larger than 54% at α = 0.01, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is larger than 54%.

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

Answer: If the population proportion of voters who prefer the Democratic candidate is 54% and if another 61 voters are surveyed then there would be a 9.68% chance that more than 62% of the 61 voters surveyed prefer the Democratic candidate.

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

Answer: If the population proportion of voters who prefer the Democratic candidate is 54% and if another 61 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 larger than 54%​​​​​​​