Problem 1. 11% 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 300 people from the inner city surveyed, 27 of them suffered from sleep apnea. What can be concluded at the level of significance of = 0.10?

1. For this study, we should use Select an answer z-test for a population proportion t-test for a population mean
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 fail to reject accept 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 10% 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 smaller than 11% and if another 300 inner city residents are surveyed then there would be a 10% chance that we would end up falsely concluding that the proportion of all inner city residents who have sleep apnea is equal to 11%.
   • There is a 10% chance that the proportion of all inner city residents who have sleep apnea is smaller than 11%.
   • If the population proportion of inner city residents who have sleep apnea is 11% and if another 300 inner city residents are surveyed then there would be a 10% chance that we would end up falsely concluding that the proportion of all inner city residents who have sleep apnea is smaller than 11%.

• There is a 13.41% chance that fewer than 11% of all inner city residents have sleep apnea.
• There is a 11% chance of a Type I error
• If the population proportion of inner city residents who have sleep apnea is 11% and if another 300 inner city residents are surveyed then there would be a 13.41% chance fewer than 9% of the 300 residents surveyed have sleep apnea.
• If the sample proportion of inner city residents who have sleep apnea is 9% and if another 300 inner city residents are surveyed then there would be a 13.41% chance of concluding that fewer than 11% of inner city residents have sleep apnea.

• The data suggest the populaton proportion is significantly smaller than 11% at = 0.10, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is smaller than 11%
• The data suggest the population proportion is not significantly smaller than 11% at = 0.10, so there is sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is equal to 11%.
• The data suggest the population proportion is not significantly smaller than 11% at = 0.10, so there is not sufficient evidence to conclude that the population proportion of inner city residents who have sleep apnea is smaller than 11%.

Problem 2. The recidivism rate for convicted sex offenders is 8%. A warden suspects that this percent is higher if the sex offender is also a drug addict. Of the 380 convicted sex offenders who were also drug addicts, 42 of them became repeat offenders. What can be concluded at the = 0.05 level of significance?

1. For this study, we should use Select an answer z-test for a population proportion t-test for a population mean
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.
   • If the population proportion of convicted sex offender drug addicts who become repeat offenders is 8% and if another 380 convicted sex offender drug addicts are observed, then there would be a 5% chance that we would end up falsely concluding that the proportion of all convicted sex offender drug addicts who become repeat offenders is higher than 8%.
   • There is a 5% chance that Lizard People aka "Reptilians" are running the world.
   • There is a 5% chance that the proportion of all convicted sex offender drug addicts who become repeat offenders is higher than 8%.
   • If the population proportion of convicted sex offender drug addicts who become repeat offenders is higher than 8% and if another 380 convicted sex offender drug addicts are observed then there would be a 5% chance that we would end up falsely concluding that the proportion of all convicted sex offender drug addicts who become repeat offenders is equal to 8%.

• If the sample proportion of convicted sex offender drug addicts who become repeat offenders is 11% and if another 380 convicted sex offender drug addicts are observed then there would be a 1.41% chance of concluding that more than 8% of all convicted sex offender drug addicts become repeat offenders.
• If the population proportion of convicted sex offender drug addicts who become repeat offenders is 8% and if another 380 convicted sex offender drug addicts are surveyed then there would be a 1.41% chance that more than 11% of the 380 convicted sex offender drug addicts in the study will become repeat offenders.
• There is a 1.41% chance of a Type I error.
• There is a 1.41% chance that more than 8% of all convicted sex offender drug addicts become repeat offenders.

• The data suggest the population proportion is not significantly higher than 8% at = 0.05, so there is statistically significant evidence to conclude that the population proportion of convicted sex offender drug addicts who become repeat offenders is equal to 8%.
• The data suggest the population proportion is not significantly higher than 8% at = 0.05, so there is statistically insignificant evidence to conclude that the population proportion of convicted sex offender drug addicts who become repeat offenders is higher than 8%.
• The data suggest the populaton proportion is significantly higher than 8% at = 0.05, so there is statistically significant evidence to conclude that the population proportion of convicted sex offender drug addicts who become repeat offenders is higher than 8%.