Reference no: EM132339448

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 314 convicted sex offenders who were also drug addicts, 44 of them became repeat offenders. What can be concluded at the α= 0.05 level of significance?

a.) for this study should we use z-test or t-test?

b.) The null and alternative hypotheses would be:   

H₀:____ ____ ____ enter as decimal

H₁:____ ____ ____ enter a decimal

c.) The test statistic ____=_____round to three decimal places

d.) the p-value=____round to four decimal places

e.) thep-value is ____α

f.) Based on this we should either fail to reject, reject or accept the null hypothesis?

g.) Thus, the final conclusion is that ...

1.) The data suggest the population proportion is not significantly higher than 9% at α = 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 9%.

2.) The data suggest the populaton proportion is significantly higher than 9% at α = 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 9%.

3.) The data suggest the population proportion is not significantly higher than 9% at α = 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 9%.

H.) Interpret the p-value in the context of the study.

1.) If the population proportion of convicted sex offender drug addicts who become repeat offenders is 9% and if another 314 convicted sex offender drug addicts are surveyed then there would be a 0.1% chance that more than 14% of the 314 convicted sex offender drug addicts in the study will become repeat offenders.

2.) There is a 0.1% chance of a Type I error.

3.) If the sample proportion of convicted sex offender drug addicts who become repeat offenders is 14% and if another 314 convicted sex offender drug addicts are observed then there would be a 0.1% chance of concluding that more than 9% of all convicted sex offender drug addicts become repeat offenders.

4.) There is a 0.1% chance that more than 9% of all convicted sex offender drug addicts become repeat offenders.

I.) Interpret the level of significance in the context of the study.

1.) There is a 5% chance that Lizard People aka "Reptilians" are running the world.

2.) If the population proportion of convicted sex offender drug addicts who become repeat offenders is higher than 9% and if another 314 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 9%.

3.) If the population proportion of convicted sex offender drug addicts who become repeat offenders is 9% and if another 314 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 9%.

4.) There is a 5% chance that the proportion of all convicted sex offender drug addicts who become repeat offenders is higher than 9%.