suppose a quality control supervisor at a paint manufacturing company suspects that the weights of paint cans on the production line are not varying in a random way, as she would expect. Instead, she suspects that the weights are either trending upward or are varying in a cyclic fashion. Every ten minutes, she randomly samples a paint can from the production line, and determines the weights of the randomly selected can. 'L' means sample falls below the median, and by U if it falls above the median. If we instead observed something like this:
U L U L U L U L U L
then the production process is showing some kind of cyclic event. In this case, we would observe more runs r than we would expect if the process were truly random. In this case, we would reject the null hypothesis of randomness, in favor of the alternative hypothesis of a cyclic effect, if r ≥ c.
Above is the context from my lecture. I don't understand the logic behind this, if we if we expect observe more runs r than the above example, don't it mean there is a stronger cyclic event? Can you show me an example(sequence of L and U) U that can be seen as "deviate from randomness"
