10.5 Rare events

Suppose you make an assumption about a property of the population (this assumption is the null hypothesis ). Then you gather sample data randomly. If the sample has properties that would be very unlikely to occur if the assumption is true, then you would conclude that your assumption about the population is probably incorrect.(Remember that your assumption is just an assumption - it is not a fact and it may or may not be true. But your sample data are real and the data are showing you a fact that seems tocontradict your assumption.)

For example, Didi and Ali are at a birthday party of a very wealthy friend. They hurry to be first in line to grab a prize from a tall basket that they cannot see inside becausethey will be blindfolded. There are 200 plastic bubbles in the basket and Didi and Ali have been told that there is only one with a $100 bill. Didi is the first person to reachinto the basket and pull out a bubble. Her bubble contains a $100 bill. The probability of this happening is $\frac{1}{200}=0.005$ . Because this is so unlikely, Ali is hoping that what the two of them were told is wrong and there are more $100 bills in thebasket. A "rare event" has occurred (Didi getting the $100 bill) so Ali doubts the assumption about only one $100 bill being in the basket.