You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly different from 67% at a level of significance of αα = 0.10. According to your sample, 52 out of 82 potential voters prefer the Democratic candidate. The test statistic ? z t  =  (please show your answer to 3 decimal places.) The p-value =  (Please show your answer to 4 decimal places.) The p-value is ? ≤ >  αα Based on this, we should Select an answer accept fail to reject reject  the null hypothesis. Thus, the final conclusion is that ... The data suggest the populaton p

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You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly different from 67% at a level of significance of αα = 0.10. According to your sample, 52 out of 82 potential voters prefer the Democratic candidate.

  1. The test statistic ? z t  =  (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 accept fail to reject reject  the null hypothesis.
  5. Thus, the final conclusion is that ...
    • The data suggest the populaton proportion is significantly different from 67% at αα = 0.10, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 67%
    • The data suggest the population proportion is not significantly different from 67% at αα = 0.10, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 67%.
    • The data suggest the population proportion is not significantly different from 67% at αα = 0.10, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 67%.
  6. Interpret the p-value in the context of the study.
    • If the sample proportion of voters who prefer the Democratic candidate is 63% and if another 82 voters are surveyed then there would be a 48.98% chance that we would conclude either fewer than 67% of all voters prefer the Democratic candidate or more than 67% of all voters prefer the Democratic candidate.
    • If the population proportion of voters who prefer the Democratic candidate is 67% and if another 82 voters are surveyed then there would be a 48.98% chance that either fewer than 63% of the 82 voters surveyed prefer the Democratic candidate or more than 71% of the 82 voters surveyed prefer the Democratic candidate.
    • There is a 48.98% chance of a Type I error.
    • There is a 48.98% chance that the percent of all voters who prefer the Democratic candidate differs from 67%.
  7. Interpret the level of significance in the context of the study.
    • There is a 10% chance that the proportion of voters who prefer the Democratic candidate is different from 67%.
    • If the population proportion of voters who prefer the Democratic candidate is 67% and if another 82 voters are surveyed then there would be a 10% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is different from 67%
    • If the proportion of voters who prefer the Democratic candidate is different from 67% and if another 82 voters are surveyed then there would be a 10% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is equal to 67%.
    • There is a 10% chance that the earth is flat and we never actually sent a man to the moon.
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