The recidivism rate for convicted sex offenders is 14%.  A warden suspects that this percent is higher if the sex offender is also a drug addict. Of the 319 convicted sex offenders who were also drug addicts, 54 of them became repeat offenders. What can be concluded at the αα = 0.01 level of significance? For this study, we should use     The null and alternative hypotheses would be:      Ho:            (please enter a decimal)     H1:            (Please enter a decimal) The test statistic     =  (please show your answer to 3 decimal places.) The p-value =  (Please show your answer to 4 decimal places.) The p-value is     αα Based on this, we should      the null hypothesis. Thus, the final conclusion is that ... The data suggest the population proportion is not significantly higher than 14% at αα = 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 14%. The data suggest the population proportion is not significantly higher than 14% at αα = 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 14%. The data suggest the populaton proportion is significantly higher than 14% at αα = 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 14%. 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 14% and if another 319 convicted sex offender drug addicts are surveyed then there would be a 6.59% chance that more than 17% of the 319 convicted sex offender drug addicts in the study will become repeat offenders. There is a 6.59% chance that more than 14% of all convicted sex offender drug addicts become repeat offenders. If the sample proportion of convicted sex offender drug addicts who become repeat offenders is 17% and if another 319 convicted sex offender drug addicts are observed then there would be a 6.59% chance of concluding that more than 14% of all convicted sex offender drug addicts become repeat offenders.  There is a 6.59% chance of a Type I error. Interpret the level of significance in the context of the study. 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 14% and if another 319 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 14%. There is a 1% chance that the proportion of all convicted sex offender drug addicts who become repeat offenders is higher than 14%. If the population proportion of convicted sex offender drug addicts who become repeat offenders is higher than 14% and if another 319 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 14%.

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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The recidivism rate for convicted sex offenders is 14%.  A warden suspects that this percent is higher if the sex offender is also a drug addict. Of the 319 convicted sex offenders who were also drug addicts, 54 of them became repeat offenders. What can be concluded at the αα = 0.01 level of significance?

  1. For this study, we should use    
  2. The null and alternative hypotheses would be:    
     Ho:            (please enter a decimal)   
     H1:            (Please enter a decimal)
  1. The test statistic     =  (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     αα
  4. Based on this, we should      the null hypothesis.
  5. Thus, the final conclusion is that ...
    • The data suggest the population proportion is not significantly higher than 14% at αα = 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 14%.
    • The data suggest the population proportion is not significantly higher than 14% at αα = 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 14%.
    • The data suggest the populaton proportion is significantly higher than 14% at αα = 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 14%.
  6. 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 14% and if another 319 convicted sex offender drug addicts are surveyed then there would be a 6.59% chance that more than 17% of the 319 convicted sex offender drug addicts in the study will become repeat offenders.
    • There is a 6.59% chance that more than 14% of all convicted sex offender drug addicts become repeat offenders.
    • If the sample proportion of convicted sex offender drug addicts who become repeat offenders is 17% and if another 319 convicted sex offender drug addicts are observed then there would be a 6.59% chance of concluding that more than 14% of all convicted sex offender drug addicts become repeat offenders.
    •  There is a 6.59% chance of a Type I error.
  7. Interpret the level of significance in the context of the study.
    • 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 14% and if another 319 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 14%.
    • There is a 1% chance that the proportion of all convicted sex offender drug addicts who become repeat offenders is higher than 14%.
    • If the population proportion of convicted sex offender drug addicts who become repeat offenders is higher than 14% and if another 319 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 14%.
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