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?

- For this study, we should use Select an answerz-test for a population proportiont-test for a population mean
- The null and alternative hypotheses would be:

Ho: ?μp Select an answer>=<≠ (please enter a decimal)

H_{1}: ?μp Select an answer≠>=< (Please enter a decimal)

- The test statistic ?zt = (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 answerrejectacceptfail to reject the null hypothesis.

Answer #1

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.

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