Question

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 383 convicted sex offenders who were

           also drug addicts, 77 of them became repeat offenders.

           a) What can be concluded at the level of significance?

b) For this study, should we use a t-test or a z-test?

c) Identify the null and alternative hypotheses.

d) If p-value is greater than should we reject or fail to reject the null hypothesis?

e) State your final conclusion.

Answer 1

a) As level of significance is not given we will assume at 5%.The level of significance will conclude that whether number of sex offender is also a drug addict is significant or not.

b)As per Central limit the sample size is sufficient large  we will use a z distribution.

c)Here null hypothesis and alternate hypothesis

and

d)First we will find test statistic

Now P-value for two tail statistic =2*P(z>2.189)=2*0.0143=0.0289

As P-value is less than assumed alpha=0.05 we reject null hypothesis.

d)If P-value is greater than alpha we failed to reject the null hypothesis

e)As we reject the null hypothesis the we support the claim that

the given percent is different if the sex offender is also a drug addict.