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You are conducting a study to see if the proportion of voters who prefer the Democratic...

You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly smaller than 55% at a level of significance of αα = 0.01. According to your sample, 26 out of 56 potential voters prefer the Democratic candidate.

  1. For this study, we should use Select an answer z-test for a population proportion t-test for a population mean
  2. The null and alternative hypotheses would be:
    Ho: ? μ p  ? ≠ < = >   (please enter a decimal)   
    H1: ? μ p  ? ≠ > = <   (Please enter a decimal)
  1. The test statistic ? t z  =  (please show your answer to 3 decimal places.)
  2. The p-value =  (Please show your answer to 4 decimal places.)
  3. The p-value is ? ≤ >  αα
  4. Based on this, we should Select an answer fail to reject reject accept  the null hypothesis.
  5. Thus, the final conclusion is that ...
    • The data suggest the populaton proportion is significantly smaller than 55% at αα = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller than 55%
    • The data suggest the population proportion is not significantly smaller than 55% at αα = 0.01, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 55%.
    • The data suggest the population proportion is not significantly smaller than 55% at αα = 0.01, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller than 55%.
  6. Interpret the p-value in the context of the study.
    • There is a 55% chance of a Type I error.
    • If the population proportion of voters who prefer the Democratic candidate is 55% and if another 56 voters are surveyed then there would be a 9.86% chance fewer than 47% of the 56 voters surveyed prefer the Democratic candidate.
    • There is a 9.86% chance that fewer than 55% of all voters prefer the Democratic candidate.
    • If the sample proportion of voters who prefer the Democratic candidate is 47% and if another 56 voters are surveyed then there would be a 9.86% chance of concluding that fewer than 55% of all voters surveyed prefer the Democratic candidate.
  7. Interpret the level of significance in the context of the study.
    • There is a 1% chance that the proportion of voters who prefer the Democratic candidate is smaller than 55%.
    • If the proportion of voters who prefer the Democratic candidate is smaller than 55% 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 55%.
    • If the population proportion of voters who prefer the Democratic candidate is 55% 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 smaller than 55%
    • There is a 1% chance that the earth is flat and we never actually sent a man to the moon.

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