The recidivism rate for convicted sex offenders is 10%. A warden suspects that this percent is lower if the sex offender is also a drug addict. Of the 321 convicted sex offenders who were also drug addicts, 26 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 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 reject accept fail to reject the null hypothesis.
7. Thus, the final conclusion is that ...

• The data suggest the population proportion is not significantly lower than 10% 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 lower than 10%.
• The data suggest the populaton proportion is significantly lower than 10% 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 lower than 10%.
• The data suggest the population proportion is not significantly lower than 10% 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 10%.

1. Interpret the p-value 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 321 inner city residents are surveyed then there would be a 12.82% chance that fewer than 8% of the 321 convicted sex offender drug addicts in the study become repeat offenders.
• There is a 12.82% chance that fewer than 10% of all convicted sex offender drug addicts become repeat offenders.
• There is a 10% chance of a Type I error.
• If the sample proportion of convicted sex offender drug addicts who become repeat offenders is 8% and if another 321 convicted sex offender drug addicts are surveyed then there would be a 12.82% chance of concluding that fewer than 10% of convicted sex offender drug addicts become repeat offenders.

1. 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 lower than 10% and if another 321 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 10%.
• 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 lower than 10%.
• If the population proportion of convicted sex offender drug addicts who become repeat offenders is 10% and if another 321 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 lower than 10%.