The recidivism rate for convicted sex offenders is 16%.  A warden suspects that this percent is different if the sex offender is also a drug addict. Of the 319 convicted sex offenders who were also drug addicts, 35 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 t-test for a population mean  The null and alternative hypotheses would be:      Ho: ? p μ  Select an answer < > ≠ =   (please enter a decimal)     H1: ? p μ  Select an answer > < ≠ =   (Please enter a decimal) The test statistic ? z t  =  (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 Select an answer fail to reject reject accept  the null hypothesis. Thus, the final conclusion is that ... The data suggest the populaton proportion is significantly different from 16% 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 16%. The data suggest the population proportion is not significantly different from 16% 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 16%. The data suggest the population proportion is not significantly different from 16% 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 16%. Interpret the p-value in the context of the study. There is a 1.42% chance of a Type I error. If the population proportion of convicted sex offender drug addicts who become repeat offenders is 16% and if another 319 convicted sex offender drug addicts are observed then there would be a 1.42% chance that either fewer than 11% of the 319 convicted sex offender drug addicts in the study become repeat offenders or more than 21% of the 319 convicted sex offender drug addicts in the study become repeat offenders. There is a 1.42% chance that the percent of all convicted sex offender drug addicts become repeat offenders differs from 16%. If the sample proportion of convicted sex offender drug addicts who become repeat offenders is 11% and if another 319 convicted sex offender drug addicts are observed, then there would be a 1.42% chance that we would conclude either fewer than 16% of all convicted sex offender drug addicts become repeat offenders or more than 16% 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 different from 16% and if another 319 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 16%. If the population proportion of convicted sex offender drug addicts who become repeat offenders is 16% and if another 319 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 offe

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The recidivism rate for convicted sex offenders is 16%.  A warden suspects that this percent is different if the sex offender is also a drug addict. Of the 319 convicted sex offenders who were also drug addicts, 35 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: ? p μ  Select an answer < > ≠ =   (please enter a decimal)   
     H1: ? p μ  Select an answer > < ≠ =   (Please enter a decimal)
  1. The test statistic ? z t  =  (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 Select an answer fail to reject reject accept  the null hypothesis.
  5. Thus, the final conclusion is that ...
    • The data suggest the populaton proportion is significantly different from 16% 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 16%.
    • The data suggest the population proportion is not significantly different from 16% 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 16%.
    • The data suggest the population proportion is not significantly different from 16% 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 16%.
  6. Interpret the p-value in the context of the study.
    • There is a 1.42% chance of a Type I error.
    • If the population proportion of convicted sex offender drug addicts who become repeat offenders is 16% and if another 319 convicted sex offender drug addicts are observed then there would be a 1.42% chance that either fewer than 11% of the 319 convicted sex offender drug addicts in the study become repeat offenders or more than 21% of the 319 convicted sex offender drug addicts in the study become repeat offenders.
    • There is a 1.42% chance that the percent of all convicted sex offender drug addicts become repeat offenders differs from 16%.
    • If the sample proportion of convicted sex offender drug addicts who become repeat offenders is 11% and if another 319 convicted sex offender drug addicts are observed, then there would be a 1.42% chance that we would conclude either fewer than 16% of all convicted sex offender drug addicts become repeat offenders or more than 16% of all convicted sex offender drug addicts become repeat offenders.
  7. 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 16% and if another 319 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 16%.
    • If the population proportion of convicted sex offender drug addicts who become repeat offenders is 16% and if another 319 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 16%.
    • 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 16%.
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