Question

You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly larger than 58% at a level of significance of αα = 0.01. According to your sample, 54 out of 86 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  Select an answer < > ≠ =   (please enter a decimal)   
   H₁: ? μ p  Select an answer ≠ < = >   (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 ? > ≤  αα
6. Based on this, we should Select an answer fail to reject accept reject  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest the population proportion is not significantly larger than 58% 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 58%.
   • The data suggest the populaton proportion is significantly larger than 58% at αα = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is larger than 58%
   • The data suggest the population proportion is not significantly larger than 58% at αα = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 58%.
8. Interpret the p-value in the context of the study.
   • If the population proportion of voters who prefer the Democratic candidate is 58% and if another 86 voters are surveyed then there would be a 18.4% chance that more than 63% of the 86 voters surveyed prefer the Democratic candidate.
   • If the sample proportion of voters who prefer the Democratic candidate is 63% and if another 86 voters are surveyed then there would be a 18.4% chance of concluding that more than 58% of all voters surveyed prefer the Democratic candidate.
   • There is a 18.4% chance that more than 58% of all voters prefer the Democratic candidate.
   • There is a 18.4% chance of a Type I error.
9. Interpret the level of significance in the context of the study.
   • If the population proportion of voters who prefer the Democratic candidate is 58% and if another 86 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 58%
   • There is a 1% chance that the proportion of voters who prefer the Democratic candidate is larger than 58%.
   • There is a 1% 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 larger than 58% and if another 86 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 58%.

Answer 1

g). The data suggest the population proportion is not significantly larger than 58% at αα = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 58%.

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