A class in New Zealand found a report suggesting that teenagers' heights in New Zealand are approximately normally distributed with a mean of 160 cm and a standard deviation of 15 cm. They thought the mean height
at their school was probably larger, so they took a random sample of n = 24 students. The mean height of
students in their sample was Ž = 166.5 cm.
To see how likely a sample like theirs was to occur by random chance alone, the class performed a simulation.
They simulated 80 samples of n = 24 heights from a normal population with a mean of 160 cm and standard
deviation of 15 cm. They recorded the mean of the heights in each sample. Here are the sample means from
their 80 samples: