The recidivism rate for convicted sex offenders is 16%. A warden suspects that this percent is higher if the sex offender is also a drug addict. Of the 318 convicted sex offenders who were also drug addicts, 54 of them became repeat offenders. What can be concluded at the αα = 0.05 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: ? μ p  Select an answer ≠ = > <   (please enter a decimal)
H₁: ? μ p  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 reject fail to reject accept  the null hypothesis.

Thus, the final conclusion is that ...

The data suggest the populaton proportion is significantly higher than 16% at αα = 0.05, 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 16%.

The data suggest the population proportion is not significantly higher than 16% at αα = 0.05, 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%.

The data suggest the population proportion is not significantly higher than 16% at αα = 0.05, 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 16%.

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 16% and if another 318 convicted sex offender drug addicts are surveyed then there would be a 31.66% chance that more than 17% of the 318 convicted sex offender drug addicts in the study will become repeat offenders.

There is a 31.66% chance that more than 16% of all convicted sex offender drug addicts become repeat offenders.

There is a 31.66% chance of a Type I error.

If the sample proportion of convicted sex offender drug addicts who become repeat offenders is 17% and if another 318 convicted sex offender drug addicts are observed then there would be a 31.66% chance of concluding that 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 higher than 16% and if another 318 convicted sex offender drug addicts are observed then there would be a 5% 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%.

There is a 5% 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 16% and if another 318 convicted sex offender drug addicts are observed, then there would be a 5% 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 16%.

There is a 5% chance that the proportion of all convicted sex offender drug addicts who become repeat offenders is higher than 16%.

Name: The recidivism rate for convicted sex offenders is 16%. A warden susp
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: The recidivism rate for convicted sex offenders is 16%. A warden suspects that this percent is higher if the sex offender is also a drug addict. Of the 318 convicted sex offenders who were also drug addicts, 54 of them became repeat offenders. What

Question

The recidivism rate for convicted sex offenders is 16%. A warden suspects that this percent is higher if the sex offender is also a drug addict. Of the 318 convicted sex offenders who were also drug addicts, 54 of them became repeat offenders. What can be concluded at the αα = 0.05 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: ? μ p Select an answer ≠ = > < (please enter a decimal)
H₁: ? μ p 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 reject fail to reject accept the null hypothesis.
Thus, the final conclusion is that ...
- The data suggest the populaton proportion is significantly higher than 16% at αα = 0.05, 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 16%.
- The data suggest the population proportion is not significantly higher than 16% at αα = 0.05, 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%.
- The data suggest the population proportion is not significantly higher than 16% at αα = 0.05, 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 16%.
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 16% and if another 318 convicted sex offender drug addicts are surveyed then there would be a 31.66% chance that more than 17% of the 318 convicted sex offender drug addicts in the study will become repeat offenders.
- There is a 31.66% chance that more than 16% of all convicted sex offender drug addicts become repeat offenders.
- There is a 31.66% chance of a Type I error.
- If the sample proportion of convicted sex offender drug addicts who become repeat offenders is 17% and if another 318 convicted sex offender drug addicts are observed then there would be a 31.66% chance of concluding that 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 higher than 16% and if another 318 convicted sex offender drug addicts are observed then there would be a 5% 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%.
- There is a 5% 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 16% and if another 318 convicted sex offender drug addicts are observed, then there would be a 5% 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 16%.
- There is a 5% chance that the proportion of all convicted sex offender drug addicts who become repeat offenders is higher than 16%.

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