You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly smaller than 51% at a level of significance of αα = 0.10. According to your sample, 41 out of 84 potential voters prefer the Democratic candidate. For this study, we should use Select an answer z-test for a population proportion t-test for a population mean  The null and alternative hypotheses would be:      Ho: ? μ p  Select an answer > < = ≠   (please enter a decimal)     H1: ? p μ  Select an answer ≠ > = <   (Please enter a decimal) The test statistic ? t z  =  (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 fail to reject reject accept  the null hypothesis. Thus, the final conclusion is that ... The data suggest the population proportion is not significantly smaller than 51% at αα = 0.10, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller than 51%. The data suggest the population proportion is not significantly smaller than 51% at αα = 0.10, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 51%. The data suggest the populaton proportion is significantly smaller than 51% at αα = 0.10, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller than 51% Interpret the p-value in the context of the study. If the population proportion of voters who prefer the Democratic candidate is 51% and if another 84 voters are surveyed then there would be a 34.4% chance fewer than 49% of the 84 voters surveyed prefer the Democratic candidate. If the sample proportion of voters who prefer the Democratic candidate is 49% and if another 84 voters are surveyed then there would be a 34.4% chance of concluding that fewer than 51% of all voters surveyed prefer the Democratic candidate.  There is a 51% chance of a Type I error. There is a 34.4% chance that fewer than 51% of all voters prefer the Democratic candidate. Interpret the level of significance in the context of the study. If the proportion of voters who prefer the Democratic candidate is smaller than 51% and if another 84 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 51%. There is a 10% chance that the earth is flat and we never actually sent a man to the moon. If the population proportion of voters who prefer the Democratic candidate is 51% and if another 84 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 smaller than 51% There is a 10% chance that the proportion of voters who prefer the Democratic candidate is smaller than 51%.

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Author:Amos Gilat
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Chapter1: Starting With Matlab
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You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly smaller than 51% at a level of significance of αα = 0.10. According to your sample, 41 out of 84 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  Select an answer > < = ≠   (please enter a decimal)   
     H1: ? p μ  Select an answer ≠ > = <   (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 population proportion is not significantly smaller than 51% at αα = 0.10, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller than 51%.
    • The data suggest the population proportion is not significantly smaller than 51% at αα = 0.10, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 51%.
    • The data suggest the populaton proportion is significantly smaller than 51% at αα = 0.10, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is smaller than 51%
  6. Interpret the p-value in the context of the study.
    • If the population proportion of voters who prefer the Democratic candidate is 51% and if another 84 voters are surveyed then there would be a 34.4% chance fewer than 49% of the 84 voters surveyed prefer the Democratic candidate.
    • If the sample proportion of voters who prefer the Democratic candidate is 49% and if another 84 voters are surveyed then there would be a 34.4% chance of concluding that fewer than 51% of all voters surveyed prefer the Democratic candidate.
    •  There is a 51% chance of a Type I error.
    • There is a 34.4% chance that fewer than 51% of all voters prefer the Democratic candidate.
  7. Interpret the level of significance in the context of the study.
    • If the proportion of voters who prefer the Democratic candidate is smaller than 51% and if another 84 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 51%.
    • There is a 10% chance that the earth is flat and we never actually sent a man to the moon.
    • If the population proportion of voters who prefer the Democratic candidate is 51% and if another 84 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 smaller than 51%
    • There is a 10% chance that the proportion of voters who prefer the Democratic candidate is smaller than 51%.
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