Question

The recidivism rate for convicted sex offenders is 12%. A warden suspects that this percent is lower if the sex offender is also a drug addict. Of the 330 convicted sex offenders who were also drug addicts, 36 of them became repeat offenders. What can be concluded at the αα = 0.05 level of significance?

1. For this study, we should use Select an answerz-test for a population proportiont-test for a population mean
2. The null and alternative hypotheses would be:
   Ho: ?μp Select an answer>=<≠ (please enter a decimal)   
   H₁: ?μp Select an answer≠>=< (Please enter a decimal)

3. The test statistic ?zt = (please show your answer to 3 decimal places.)
4. The p-value = (Please show your answer to 4 decimal places.)
5. The p-value is ?≤> αα
6. Based on this, we should Select an answerrejectacceptfail to reject the null hypothesis.

Answer 1

Proportion = 0.12
Total number of sample (n) = 330
number of favourable events (X) = 36

We are interested in testing the hypothesis

Since P-value of a two tailed test is equal to

P = (0.2709971507595857)
P = 0.271
Here, the P-value is greater than the level of significance 0.05; Fail to reject the null hypothesis
Since, the test is two-tail test at

Decision Rule: Reject the null hypothesis if the test statistic value is less than the critical value -1.96 or greater than the critical value 1.96
The statistic value, -0.6098 is greater than the critical values -1.96 . Therefore, we fail to reject the null hypothesis.