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%.

Question

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%.

Accepted Answer

The provided data is,

The sample proportion is,