8% 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 311 people from the inner city surveyed, 16 of them suffered from sleep apnea. What can be concluded at the level of significance of = 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: ? p Select an answer < = > (please enter a decimal) H₁: ? p 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 ? >
6. Based on this, we should Select an answer accept fail to reject reject the null hypothesis.
7. Thus, the final conclusion is that ...
8. Interpret the p-value in the context of the study.
9. Interpret the level of significance in the context of the study.
   • If the population proportion of inner city residents who have sleep apnea is 8% and if another 311 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 smaller than 8%.
   • There is a 5% chance that the proportion of all inner city residents who have sleep apnea is smaller than 8%.
   • If the population proportion of inner city residents who have sleep apnea is smaller than 8% and if another 311 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 8%.
   • 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.

• If the population proportion of inner city residents who have sleep apnea is 8% and if another 311 inner city residents are surveyed then there would be a 3.17% chance fewer than 5% of the 311 residents surveyed have sleep apnea.
• If the sample proportion of inner city residents who have sleep apnea is 5% and if another 311 inner city residents are surveyed then there would be a 3.17% chance of concluding that fewer than 8% of inner city residents have sleep apnea.
• There is a 3.17% chance that fewer than 8% of all inner city residents have sleep apnea.
• There is a 8% chance of a Type I error

• The data suggest the populaton proportion is significantly smaller than 8% at = 0.05, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is smaller than 8%
• The data suggest the population proportion is not significantly smaller than 8% at = 0.05, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is equal to 8%.
• The data suggest the population proportion is not significantly smaller than 8% at = 0.05, so there is not sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is smaller than 8%.