The recidivism rate for convicted sex offenders is 9%.  A warden suspects that this percent is higher if the sex offender is also a drug addict. Of the 362 convicted sex offenders who were also drug addicts, 36 of them became repeat offenders. What can be concluded at the αα = 0.10 level of significance? Thus, the final conclusion is that ... The data suggest the population proportion is not significantly higher than 9% 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 higher than 9%. The data suggest the population proportion is not significantly higher than 9% 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 9%. The data suggest the populaton proportion is significantly higher than 9% 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 higher than 9%. 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 10% and if another 362 convicted sex offender drug addicts are observed then there would be a 26.5% chance of concluding that more than 9% of all convicted sex offender drug addicts become repeat offenders.  There is a 26.5% chance of a Type I error. If the population proportion of convicted sex offender drug addicts who become repeat offenders is 9% and if another 362 convicted sex offender drug addicts are surveyed then there would be a 26.5% chance that more than 10% of the 362 convicted sex offender drug addicts in the study will become repeat offenders. There is a 26.5% chance that more than 9% of all convicted sex offender drug addicts become repeat offenders. 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 higher than 9% and if another 362 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 9%. There is a 10% chance that the proportion of all convicted sex offender drug addicts who become repeat offenders is higher than 9%. There is a 10% 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 9% and if another 362 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 higher than 9%.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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The recidivism rate for convicted sex offenders is 9%.  A warden suspects that this percent is higher if the sex offender is also a drug addict. Of the 362 convicted sex offenders who were also drug addicts, 36 of them became repeat offenders. What can be concluded at the αα = 0.10 level of significance?

  1. Thus, the final conclusion is that ...
    • The data suggest the population proportion is not significantly higher than 9% 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 higher than 9%.
    • The data suggest the population proportion is not significantly higher than 9% 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 9%.
    • The data suggest the populaton proportion is significantly higher than 9% 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 higher than 9%.
  2. 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 10% and if another 362 convicted sex offender drug addicts are observed then there would be a 26.5% chance of concluding that more than 9% of all convicted sex offender drug addicts become repeat offenders.
    •  There is a 26.5% chance of a Type I error.
    • If the population proportion of convicted sex offender drug addicts who become repeat offenders is 9% and if another 362 convicted sex offender drug addicts are surveyed then there would be a 26.5% chance that more than 10% of the 362 convicted sex offender drug addicts in the study will become repeat offenders.
    • There is a 26.5% chance that more than 9% of all convicted sex offender drug addicts become repeat offenders.
  3. 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 higher than 9% and if another 362 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 9%.
    • There is a 10% chance that the proportion of all convicted sex offender drug addicts who become repeat offenders is higher than 9%.
    • There is a 10% 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 9% and if another 362 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 higher than 9%.
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