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 395 convicted sex offenders who were also drug addicts, 40 of them became repeat offenders. What can be concluded at the αα = 0.10 level of significance? For this study, we should use: Select an answer? z-test for a population proportion or  t-test for a population mean ? The null and alternative hypotheses would be:     Ho:  μ or p?  Select an answer: < > = ≤ ≥ ≠?  ______ (please enter a decimal)    H1:  p or μ? Select an answer: > < ≥ = ≤ ≠? _____   (Please enter a decimal) The test statistic: t or z?  =_______  (please show your answer to 3 decimal places.) The p-value =_________?  (Please show your answer to 4 decimal places.) The p-value is ? ≤ or  >?  Based on this, we should? Select an answer: reject? fail to reject?  or accept?  the null hypothesis. 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 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%. 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%. Interpret the p-value in the context of the study.  There is a 21.7% chance of a Type I error. If the sample proportion of convicted sex offender drug addicts who become repeat offenders is 10% and if another 395 convicted sex offender drug addicts are observed then there would be a 21.7% chance of concluding that more than 9% 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 9% and if another 395 convicted sex offender drug addicts are surveyed then there would be a 21.7% chance that more than 10% of the 395 convicted sex offender drug addicts in the study will become repeat offenders. There is a 21.7% 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. 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 higher than 9% and if another 395 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%. If the population proportion of convicted sex offender drug addicts who become repeat offenders is 9% and if another 395 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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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 395 convicted sex offenders who were also drug addicts, 40 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 or  t-test for a population mean ?
  2. The null and alternative hypotheses would be:    
     Ho:  μ or p?  Select an answer: < > = ≤ ≥ ≠?  ______ (please enter a decimal)   
     H1:  p or μ? Select an answer: > < ≥ = ≤ ≠? _____   (Please enter a decimal)
  1. The test statistic: t or z?  =_______  (please show your answer to 3 decimal places.)
  2. The p-value =_________?  (Please show your answer to 4 decimal places.)
  3. The p-value is ? ≤ or  >? 
  4. Based on this, we should? Select an answer: reject? fail to reject?  or accept?  the null hypothesis.
  5. 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 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%.
    • 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%.
  6. Interpret the p-value in the context of the study.
    •  There is a 21.7% chance of a Type I error.
    • If the sample proportion of convicted sex offender drug addicts who become repeat offenders is 10% and if another 395 convicted sex offender drug addicts are observed then there would be a 21.7% chance of concluding that more than 9% 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 9% and if another 395 convicted sex offender drug addicts are surveyed then there would be a 21.7% chance that more than 10% of the 395 convicted sex offender drug addicts in the study will become repeat offenders.
    • There is a 21.7% chance that more than 9% of all convicted sex offender drug addicts become repeat offenders.
  7. Interpret the level of significance in the context of the study.
    • 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 higher than 9% and if another 395 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%.
    • If the population proportion of convicted sex offender drug addicts who become repeat offenders is 9% and if another 395 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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