The owners of Shoppers Food Warehouse (SFW) believe that their store detective is a lazy, shiftless, donut-eating slug. They want to determine whether he is ignoring the problem of shoplifting.

a. On a day with 9 shoppers in the store, the SFW detective identifies 1 shoplifter. Given your probability distribution, what is the probability that this would occur?

b. Perform a hypothesis test at the 5% significance level testing the null hypothesis that the probability the SFW store detective catches a shoplifter is .36 against the alternative hypothesis that the probability is less than that. Given that the store detective catches only one shoplifter, should the storeowners fire the SFW detective? Why or why not? (Note: p = detective catches a shoplifter = .36)

Be sure to show the five steps of hypothesis testing.