You are mostly seniors, and will be graduating in May. Imagine that upon graduation, you are offered a job with a pharmaceutical company for an exorbitant salary. The first week on the job, your supervisor asks you to run an experiment to tell whether a drug the company is developing increases the concentration of a certain steroid in the liver of pigs. This steroid has been implicated as a possible carcinogen.
You go to the lab, have your technician feed some of the drug to a pig, and then later have your technician euthanize the pig and cut out its liver. She also does this to another pig that has not been given the drug. You measure the amount of steroid in the livers of the two pigs. The liver of the non-drug pig has 25.75 mg/kg of steroid; the liver of the drug pig has 30.8 mg/kg of steroid. You go to the supervisor and say, "Sorry, you can't sell this drug. It causes cancer in pigs" Your supervisor smiles and says "Good joke, now get back to the lab and bring me some quantitative data".
On your way back to the lab, it dawns on you that all pigs' livers might not respond the same way to the drug. Some may take up more of the drug from the blood, some may produce more of the steroid than others in response to the drug, some may break down the steroid more rapidly, some may retain it longer in the liver cells. So you have your technician give the drug to 30 pigs, and use 30 more as controls -- you treat them the same way but don't give them any drugs. Later you have the tech euthanize all of the pigs, and you measure the amount of steroid in their livers. You add up the readings you get and divide by the number of pigs. The average amount of steroid in the livers of the non-drug pigs is 25.75 mg/kg; the average amount in the drug pig livers is 30.8 mg/kg. You go back to the supervisor and say "Look! I was right! You can't sell this drug, it causes cancer in pigs." Your supervisor says "Listen, this company has 5.4 million dollars invested in this drug. You go back to the lab and give me some data that will get it past the FDA or you're fired." This time, as you are going back to the lab, you have more difficulty thinking about statistics because you are thinking about how you are going to pay for that shiny new Lexus. Fortunately, some dim memory from college biology sneaks into your consciousness, and you think, gee how do I know that the pigs livers are really different in steroid concentration? So you go back to the lab and ask your technician to run a t-test on the pig liver data. You then sit at your desk biting your nails, until he comes back and says "You're going to owe me big for a long time. These data are just what you want." He throws a sheet of paper on your desk that is covered with equations and computations which you do not understand. So you have to beg him to explain it to you. He says "Look, the means are 25.75 and 30.8, right? But the variances are 61.25 and 72.8, so the t value is 1.95, and the probability that the means are the same is greater than 5%. This is not statistically significant, so the FDA will allow the company to sell the drug and the supervisor will be off your back and you can keep your car. So now you really owe me big." Fortunately, you learned enough statistics in college to BS your way through your next meeting with your supervisor, who doesn't know much more about statistics than you do, and you will be in a better job at another company before anyone finds out how ignorant you were about statistics in the first place. And you get to keep your car.