Question

The recidivism rate for convicted sex offenders is 11%. A warden suspects that this percent is different if the sex offender is also a drug addict. Of the 366 convicted sex offenders who were also drug addicts, 26 of them became repeat offenders. What can be concluded at the αα = 0.10 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: ? μ p  Select an answer ≥ = < ≤ > ≠   (please enter a decimal)   
   H₁: ? p μ  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 ? > ≤  αα
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 different from 11% at αα = 0.10, so there is statistically insignificant evidence to conclude that the population proportion of convicted sex offender drug addicts who become repeat offenders is different from 11%.
   • The data suggest the population proportion is not significantly different from 11% at αα = 0.10, 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 11%.
   • The data suggest the populaton proportion is significantly different from 11% at αα = 0.10, so there is statistically significant evidence to conclude that the population proportion of convicted sex offender drug addicts who become repeat offenders is different from 11%.
8. 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 11% and if another 366 convicted sex offender drug addicts are observed then there would be a 1.72% chance that either fewer than 7% of the 366 convicted sex offender drug addicts in the study become repeat offenders or more than 15% of the 366 convicted sex offender drug addicts in the study become repeat offenders.
   • There is a 1.72% chance of a Type I error.
   • If the sample proportion of convicted sex offender drug addicts who become repeat offenders is 7% and if another 366 convicted sex offender drug addicts are observed, then there would be a 1.72% chance that we would conclude either fewer than 11% of all convicted sex offender drug addicts become repeat offenders or more than 11% of all convicted sex offender drug addicts become repeat offenders.
   • There is a 1.72% chance that the percent of all convicted sex offender drug addicts become repeat offenders differs from 11%.
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 different from 11% and if another 366 convicted sex offender drug addicts are observed then there would be a 10% 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 11%.
   • There is a 10% chance that Lizard People aka "Reptilians" are running the world.
   • There is a 10% chance that the proportion of all convicted sex offender drug addicts who become repeat offenders is different from 11%.
   • If the population proportion of convicted sex offender drug addicts who become repeat offenders is 11% and if another 366 convicted sex offender drug addicts are observed, then there would be a 10% chance that we would end up falsely concluding that the proportion of all convicted sex offender drug addicts who become repeat offenders is different from 11%.

Answer 1

e) Ans: The data suggest the populaton proportion is significantly different from 11% at αα = 0.10, so there is statistically significant evidence to conclude that the population proportion of convicted sex offender drug addicts who become repeat offenders is different from 11%.