10% 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 328 people from the inner city surveyed, 26 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:

H0: ( or p )_____________ Select an answer (= > < ) ___________

H1: ( or p ) _____________ Select an answer (= > < ) ___________

3. The test statistic ( z or t ) = _____________________ (please show your answer to 3 decimal places.)

1. The p-value = __________________ (Please show your answer to 4 decimal places.)
2. The p-value is ( or >) ____________
3. Based on this, we should Select an answer ( reject, accept or fail to reject) the null hypothesis. ______________

1. Thus, the final conclusion is that ...
   • The data suggest the population proportion is not significantly smaller than 10% 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 10%.
   • The data suggest the populaton proportion is significantly smaller than 10% 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 10%
   • The data suggest the population proportion is not significantly smaller than 10% 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 10%.
2. Interpret the p-value in the context of the study.
   • If the sample proportion of inner city residents who have sleep apnea is 8% and if another 328 inner city residents are surveyed then there would be a 10.54% chance of concluding that fewer than 10% of inner city residents have sleep apnea.
   • There is a 10.54% chance that fewer than 10% of all inner city residents have sleep apnea.
   • There is a 10% chance of a Type I error
   • If the population proportion of inner city residents who have sleep apnea is 10% and if another 328 inner city residents are surveyed then there would be a 10.54% chance fewer than 8% of the 328 residents surveyed have sleep apnea.
3. 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 smaller than 10%.
   • If the population proportion of inner city residents who have sleep apnea is smaller than 10% and if another 328 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 10%.
   • 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 10% and if another 328 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 10%.

The recidivism rate for convicted sex offenders is 10%. A warden suspects that this percent is higher if the sex offender is also a drug addict. Of the 372 convicted sex offenders who were also drug addicts, 41 of them became repeat offenders. What can be concluded at the = 0.01 level of significance?

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:

H0: ( or p )_____________ Select an answer (= > < ) ___________

H1: ( or p ) _____________ Select an answer (= > < ) ___________

3. The test statistic ( z or t ) = _____________________ (please show your answer to 3 decimal places.)

1. The p-value = __________________ (Please show your answer to 4 decimal places.)
2. The p-value is ( or >) ____________
3. Based on this, we should Select an answer ( reject, accept or fail to reject) the null hypothesis. ______________
4. Thus, the final conclusion is that ...
   • The data suggest the population proportion is not significantly higher than 10% at = 0.01, 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 10%.
   • The data suggest the populaton proportion is significantly higher than 10% at = 0.01, 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 10%.
   • The data suggest the population proportion is not significantly higher than 10% at = 0.01, 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 10%.
5. Interpret the p-value in the context of the study.

• If the sample proportion of convicted sex offender drug addicts who become repeat offenders is 11% and if another 372 convicted sex offender drug addicts are observed then there would be a 25.57% chance of concluding that more than 10% 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 10% and if another 372 convicted sex offender drug addicts are surveyed then there would be a 25.57% chance that more than 11% of the 372 convicted sex offender drug addicts in the study will become repeat offenders.
• There is a 25.57% chance that more than 10% of all convicted sex offender drug addicts become repeat offenders.
• There is a 25.57% chance of a Type I error.

6. 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 10% and if another 372 convicted sex offender drug addicts are observed, then there would be a 1% 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 10%.
• There is a 1% chance that Lizard People aka "Reptilians" are running the world.
• If the population proportion of convicted sex offender drug addicts who become repeat offenders is higher than 10% and if another 372 convicted sex offender drug addicts are observed then there would be a 1% 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 10%.
• There is a 1% chance that the proportion of all convicted sex offender drug addicts who become repeat offenders is higher than 10%.

Only about 20% of all people can wiggle their ears. Is this percent different for millionaires? Of the 343 millionaires surveyed, 48 could wiggle their ears. What can be concluded at the = 0.01 level of significance?

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:

H0: ( or p )_____________ Select an answer (= > < ) ___________

H1: ( or p ) _____________ Select an answer (= > < ) ___________

3. The test statistic ( z or t ) = _____________________ (please show your answer to 3 decimal places.)

1. The p-value = __________________ (Please show your answer to 4 decimal places.)
2. The p-value is ( or >) ____________
3. Based on this, we should Select an answer ( reject, accept or fail to reject) the null hypothesis. ______________
4. Thus, the final conclusion is that ..

• The data suggest the population proportion is not significantly different from 20% at = 0.01, so there is statistically significant evidence to conclude that the population proportion of millionaires who can wiggle their ears is equal to 20%.
• The data suggest the population proportion is not significantly different from 20% at = 0.01, so there is statistically insignificant evidence to conclude that the population proportion of millionaires who can wiggle their ears is different from 20%.
• The data suggest the populaton proportion is significantly different from 20% at = 0.01, so there is statistically significant evidence to conclude that the population proportion of millionaires who can wiggle their ears is different from 20%.