46 CHAPTER 4 Did We Meet or Exceed Our Goal? Example 1 During an early stage design test eight out of nine users successfully completed a task. Is there sufficient evidence to conclude that at least 70% of all users would be able to complete the same task? We have an observed completion rate of 8/9 = 88.9%. Using the exact probabilities from the binomial we can find the probability of obtaining eight or more successes out of nine trials if the population comple- tion rate is 70%. To do so we find the probability of getting exactly eight successes and the probability of getting exactly nine successes: pð8Þ = 9! 0:7 8 ð1 - 0:7Þ ð9-8Þ = 9! 0:0576ð0:3Þ ð1Þ = 9ð0:01729Þ = 0:1556 8!ð9 - 8Þ! 8!ð1!Þ pð9Þ = In Excel: 9! 9! 0:7 9 ð1 - 0:7Þ ð9-9Þ = 0:04035ð0:3Þ ð0Þ = 0:04035ð1Þ = 0:04035 9!ð9 - 9Þ! 9!ð1Þ = BINOMDISTð8,9,0:7,FALSEÞ = 0:1556 = BINOMDISTð9,9,0:7,FALSEÞ = 0:04035