13% of all Americans suffer from sleep apnea. A researcher suspects that a lower percentage of those who live in the inner city have sleep apnea. Of the 324 people from the inner city surveyed, 32 of...

13% of all Americans suffer from sleep apnea. A researcher suspects that a lower percentage of those who live in the inner city have sleep apnea. Of the 324 people from the inner city surveyed, 32 of them suffered from sleep apnea. What can be concluded at the level of significance of αα = 0.01?

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: ? p μ  ? = < > ≠  (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 accept fail to reject reject  the null hypothesis.


5. Thus, the final conclusion is that ...
   
   
   

   
   
   • The data suggest the population proportion is not
     significantly
     smaller than 13% at αα = 0.01, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is equal to 13%.
   
   
   • The data suggest the population proportion is not
     significantly
     smaller than 13% at αα = 0.01, so there is not sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is smaller than 13%.
   
   
   • The data suggest the populaton proportion is
     significantly
     smaller than 13% at αα = 0.01, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is smaller than 13%
   
   

   
   
   
   


6. Interpret the p-value in the context of the study.
   
   
   

   
   
   • If the population proportion of inner city residents who have sleep apnea is 13% and if another 324 inner city residents are surveyed then there would be a 4.73% chance fewer than 10% of the 324 residents surveyed have sleep apnea.
   
   
   • If the sample proportion of inner city residents who have sleep apnea is 10% and if another 324 inner city residents are surveyed then there would be a 4.73% chance of concluding that fewer than 13% of inner city residents have sleep apnea.
   
   
   • There is a 4.73% chance that fewer than 13% of all inner city residents have sleep apnea.
   
   
   • There is a 13% chance of a Type I error
   
   

   
   
   
   


7. Interpret the level of significance in the context of the study.
   
   
   

   
   
   • If the population proportion of inner city residents who have sleep apnea is smaller than 13% and if another 324 inner city residents are surveyed then there would be a 1% chance that we would end up falsely concluding that the proportion of all inner city residents who have sleep apnea is equal to 13%.
   
   
   • If the population proportion of inner city residents who have sleep apnea is 13% and if another 324 inner city residents are surveyed then there would be a 1% chance that we would end up falsely concluding that the proportion of all inner city residents who have sleep apnea is smaller than 13%.
   
   
   • There is a 1% chance that the proportion of all inner city residents who have sleep apnea is smaller than 13%.
   
   
   • There is a 1% chance that aliens have secretly taken over the earth and have cleverly disguised themselves as the presidents of each of the countries on earth.