Hypothesis testing of single proportion and hypothesis testing of equality of two means.
1. National figures reveal that the possibility of a youth offender on probation committing another crime is 0.80. (This is called "recidivism.") After a special government program intended to reduce recidivism is put in place, a sample of 100 young offenders enrolled in the program reveals that 70 subsequently committed another crime. You are asked to make a judgment about whether government funds invested in this program have succeeded in reducing crime.
1. State the null and alternative hypotheses.
2. Compute the value of the test statistic.
3. Taking alpha=.01, conduct a hypothesis test using the pvalue technique.
2. Independent random samples of 400 observations each were selected from two populations, giving the following results:
Sample 1

Sample 2

= 5,275

= 5,240

s_{1}=150

s_{2}=200

You want to know whether the population means are different in the two populations. Conduct a hypothesis test using an alpha of .05 and the critical value method. (Be sure to clearly state your null and alternative hypothesis, the value of your test statistic, the critical value(s) you compare it to, and your conclusion.)