Question

A friend of yours is excited about the results of an evaluation of a new rehabilitation program for adult prison inmates. She compared a sample of released prisoners who completed the program while they were incarcerated to a sample who did not, and she found that 21% of the treatment group was rearrested within one year of release, compared to 36% of the no-treatment group. She asserts that this is a definitive proof that the program works. What should you tell your friend?The chapter is about Hypothesis testing: A conceptual introduction

Answer 1

I will tell my friend that we can't really directly conclude from the proportions that the program definitely works. We first need to lay down a hypothesis testing procedure and consider that the program is not effective (which would be our null hypothesis) until it is proven to be effective (which would be our alternate hypothesis).

We need to calculate the probability given that the null hypothesis is true. This will tell us that what is the probability that this result didn't occur by mere chance. If the p-value is very less (maybe less than 0.05), we can say that this result did not occur due to chance or the probability of Ho occuring is very low and hence we can reject the null hypothesis. Therefore, we will consider the alternative hypothesis to be the more likely scenario. To calculate the p-value, we need to run the independent samples proportion test, calculate the statistic and the p-value. In this way, we can do the hypothesis testing and come to a conclusion.