You are conducting a study to see if the proportion of voters who prefer the Democratic candidate is significantly different from 57% at a level of significance of α = 0.10. According to your sample, 53 out of 96 potential voters prefer the Democratic candidate. For this study, we should use The null and alternative hypotheses would be:      Ho: (please enter a decimal)     H1: (Please enter a decimal) The test statistic   = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is α   Based on this, we should the null hypothesis. Thus, the final conclusion is that ... The data suggest the population proportion is not significantly different from 57% at α = 0.10, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 57%. The data suggest the populaton proportion is significantly different from 57% at α = 0.10, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 57% The data suggest the population proportion is not significantly different from 57% at α   = 0.10, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 57%. Interpret the p-value in the context of the study. There is a 72.3% chance that the percent of all voters who prefer the Democratic candidate differs from 57%. If the sample proportion of voters who prefer the Democratic candidate is 55% and if another 96 voters are surveyed then there would be a 72.3% chance that we would conclude either fewer than 57% of all voters prefer the Democratic candidate or more than 57% of all voters prefer the Democratic candidate. If the population proportion of voters who prefer the Democratic candidate is 57% and if another 96 voters are surveyed then there would be a 72.3% chance that either fewer than 55% of the 96 voters surveyed prefer the Democratic candidate or more than 59% of the 96 voters surveyed prefer the Democratic candidate. There is a 72.3% chance of a Type I error. Interpret the level of significance in the context of the study. If the population proportion of voters who prefer the Democratic candidate is 57% and if another 96 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 57% If the proportion of voters who prefer the Democratic candidate is different from 57% and if another 96 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 57%. There is a 10% chance that the earth is flat and we never actually sent a man to the moon. There is a 10% chance that the proportion of voters who prefer the Democratic candidate is different from 57%.

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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 different from 57% at a level of significance of α

= 0.10. According to your sample, 53 out of 96 potential voters prefer the Democratic candidate.

  1. For this study, we should use

The null and alternative hypotheses would be:    
 Ho: (please enter a decimal)   
 H1:

  1. (Please enter a decimal)
  1. The test statistic

 

  • = (please show your answer to 3 decimal places.)
  • The p-value = (Please show your answer to 4 decimal places.)
  • The p-value is

α

  •  
  • Based on this, we should
  • the null hypothesis.
  • Thus, the final conclusion is that ...
    • The data suggest the population proportion is not significantly different from 57% at α
  • = 0.10, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is equal to 57%.
  • The data suggest the populaton proportion is significantly different from 57% at α
  • = 0.10, so there is sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 57%
  • The data suggest the population proportion is not significantly different from 57% at α

 

    • = 0.10, so there is not sufficient evidence to conclude that the proportion of voters who prefer the Democratic candidate is different from 57%.
  1. Interpret the p-value in the context of the study.
    • There is a 72.3% chance that the percent of all voters who prefer the Democratic candidate differs from 57%.
    • If the sample proportion of voters who prefer the Democratic candidate is 55% and if another 96 voters are surveyed then there would be a 72.3% chance that we would conclude either fewer than 57% of all voters prefer the Democratic candidate or more than 57% of all voters prefer the Democratic candidate.
    • If the population proportion of voters who prefer the Democratic candidate is 57% and if another 96 voters are surveyed then there would be a 72.3% chance that either fewer than 55% of the 96 voters surveyed prefer the Democratic candidate or more than 59% of the 96 voters surveyed prefer the Democratic candidate.
    • There is a 72.3% chance of a Type I error.
  2. Interpret the level of significance in the context of the study.
    • If the population proportion of voters who prefer the Democratic candidate is 57% and if another 96 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 57%
    • If the proportion of voters who prefer the Democratic candidate is different from 57% and if another 96 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 57%.
    • There is a 10% chance that the earth is flat and we never actually sent a man to the moon.
    • There is a 10% chance that the proportion of voters who prefer the Democratic candidate is different from 57%.

 

 
 
 
 
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