Question

15% of all Americans suffer from sleep apnea. A researcher suspects that a higher percentage of those who live in the inner city have sleep apnea. Of the 314 people from the inner city surveyed, 50 of them suffered from sleep apnea. What can be concluded at the level of significance of αα = 0.05?

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: ? p μ  Select an answer = < ≠ >   (Please enter a decimal)

3. The test statistic ? z t  =  (please show your answer to 3 decimal places.)
4. The p-value =  (Please show your answer to 4 decimal places.)
5. The p-value is ? > ≤  αα
6. Based on this, we should Select an answer reject fail to reject accept  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest the populaton proportion is significantly larger than 15% at αα = 0.05, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is larger than 15%
   • The data suggest the population proportion is not significantly larger than 15% at αα = 0.05, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is equal to 15%.
   • The data suggest the population proportion is not significantly larger than 15% at αα = 0.05, so there is not sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is larger than 15%.
8. Interpret the p-value in the context of the study.
   • If the population proportion of inner city residents who have sleep apnea is 15% and if another 314 inner city residents are surveyed then there would be a 32.34% chance that more than 16% of the 314 inner city residents surveyed have sleep apnea.
   • There is a 32.34% chance that more than 15% of all inner city residents have sleep apnea.
   • There is a 32.34% chance of a Type I error.
   • If the sample proportion of inner city residents who have sleep apnea is 16% and if another 314 inner city residents are surveyed then there would be a 32.34% chance of concluding that more than 15% of all inner city residents have sleep apnea.
9. Interpret the level of significance in the context of the study.
   • There is a 5% chance that the proportion of all inner city residents who have sleep apnea is larger than 15%.
   • If the population proportion of inner city residents who have sleep apnea is 15% and if another 314 inner city residents are surveyed then there would be a 5% chance that we would end up falsely concluding that the proportion of all inner city residents who have sleep apnea is larger than 15%.
   • If the population proportion of inner city residents who have sleep apnea is larger than 15% and if another 314 inner city residents are surveyed then there would be a 5% chance that we would end up falsely concluding that the proportion of all inner city residents who have sleep apnea is equal to 15%.
   • There is a 5% chance that aliens have secretly taken over the earth and have cleverly disguised themselves as the presidents of each of the countries on earth.

Answer 1

(e) The data suggest the population proportion is not significantly larger than 15% at αα = 0.05, so there is not sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is larger than 15%.

(f) There is a 32.34% chance that more than 15% of all inner city residents have sleep apnea.

(g) If the population proportion of inner city residents who have sleep apnea is 15% and if another 314 inner city residents are surveyed then there would be a 5% chance that we would end up falsely concluding that the proportion of all inner city residents who have sleep apnea is larger than 15%.