16% of all Americans suffer from sleep apnea. A researcher suspects that a different percentage of those who live in the inner city have sleep apnea. Of the 312 people from the inner city surveyed, 44 of them suffered from sleep apnea. What can be concluded at the level of significance of = 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 Select an answer < = > (please enter a decimal) H₁: ? p Select an answer > = < (Please enter a decimal)
3. The test statistic ? t z = (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.
   • There is a 1% chance that the proportion of all inner city residents who have sleep apnea is different from 16%.
   • 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.
   • If the population proportion of inner city residents who have sleep apnea is different from 16% and if another 312 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 16%.
   • If the population proportion of inner city residents who have sleep apnea is 16% and if another 312 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 different from 16%.

• If the population proportion of inner city residents who have sleep apnea is 16% and if another 312 inner city residents are surveyed then there would be a 36.06% chance that either fewer than 14% of the 312 inner city residents surveyed have sleep apnea or more than 18% of the 312 inner city residents have sleep apnea.
• There is a 36.06% chance that the percent of all inner city residents have sleep apnea differs from 16%.
• There is a 36.06% chance of a Type I error.
• If the sample proportion of inner city residents who have sleep apnea is 14% and if another 312 inner city residents are surveyed then there would be a 36.06% chance that we would conclude either fewer than 16% of all inner city residents have sleep apnea or more than 16% of all inner city residents have sleep apnea.

• The data suggest the population proportion is not significantly different from 16% at = 0.01, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is equal to 16%.
• The data suggest the populaton proportion is significantly different from 16% at = 0.01, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is different from 16%
• The data suggest the population proportion is not significantly different from 16% at = 0.01, so there is not sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is different from 16%.