You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly larger than 80% at a level of significance of αα = 0.05. According to your sample, 59 out of 67 potential voters prefer the Democratic candidate. For this study, we should use Select an answer t-test for a population mean z-test for a population proportion  The null and alternative hypotheses would be:      Ho: ? μ p  Select an answer = > ≠ <   (please enter a decimal)     H1: ? μ p  Select an answer ≠ = < >   (Please enter a decimal) 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 proportion is significantly larger than 80% at αα = 0.05, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is larger than 80% The data suggest the population proportion is not significantly larger than 80% at αα = 0.05, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is larger than 80%. The data suggest the population proportion is not significantly larger than 80% at αα = 0.05, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 80%. Interpret the p-value in the context of the study. If the population proportion of voters who prefer the Democratic candidate is 80% and if another 67 voters are surveyed then there would be a 4.95% chance that more than 88% of the 67 voters surveyed prefer the Democratic candidate.  There is a 4.95% chance of a Type I error. There is a 4.95% chance that more than 80% of all voters prefer the Democratic candidate. If the sample proportion of voters who prefer the Democratic candidate is 88% and if another 67 voters are surveyed then there would be a 4.95% chance of concluding that more than 80% of all voters surveyed prefer the Democratic candidate. Interpret the level of significance in the context of the study. There is a 5% chance that the proportion of voters who prefer the Democratic candidate is larger than 80%. If the proportion of voters who prefer the Democratic candidate is larger than 80% and if another 67 voters are surveyed then there would be a 5% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is equal to 80%. If the population proportion of voters who prefer the Democratic candidate is 80% and if another 67 voters are surveyed then there would be a 5% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is larger than 80% There is a 5% chance that the earth is flat and we never actually sent a man to the moon.

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You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly larger than 80% at a level of significance of αα = 0.05. According to your sample, 59 out of 67 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: ? μ p  Select an answer = > ≠ <   (please enter a decimal)   
     H1: ? μ p  Select an answer ≠ = < >   (Please enter a decimal)
  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 larger than 80% at αα = 0.05, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is larger than 80%
    • The data suggest the population proportion is not significantly larger than 80% at αα = 0.05, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is larger than 80%.
    • The data suggest the population proportion is not significantly larger than 80% at αα = 0.05, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 80%.
  6. Interpret the p-value in the context of the study.
    • If the population proportion of voters who prefer the Democratic candidate is 80% and if another 67 voters are surveyed then there would be a 4.95% chance that more than 88% of the 67 voters surveyed prefer the Democratic candidate.
    •  There is a 4.95% chance of a Type I error.
    • There is a 4.95% chance that more than 80% of all voters prefer the Democratic candidate.
    • If the sample proportion of voters who prefer the Democratic candidate is 88% and if another 67 voters are surveyed then there would be a 4.95% chance of concluding that more than 80% of all voters surveyed prefer the Democratic candidate.
  7. Interpret the level of significance in the context of the study.
    • There is a 5% chance that the proportion of voters who prefer the Democratic candidate is larger than 80%.
    • If the proportion of voters who prefer the Democratic candidate is larger than 80% and if another 67 voters are surveyed then there would be a 5% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is equal to 80%.
    • If the population proportion of voters who prefer the Democratic candidate is 80% and if another 67 voters are surveyed then there would be a 5% chance that we would end up falsely concluding that the proportion of voters who prefer the Democratic candidate is larger than 80%
    • There is a 5% chance that the earth is flat and we never actually sent a man to the moon.

 

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