Hypothesis Testing

Even though we found that the mean height of the nine 18-year-old men in our sample, which was 181.11 cm, was higher than the expected value of 180 cm, we cannot conclusively state that men are taller than expected (e.g., taller now than they were previously). We must also consider the uncertainty associated with having a small sample and the fact that there is some variability (the standard deviation is not zero) in our sample. To test whether the mean value we found is high enough to conclude that 18-year-old men are taller now than before, we can conduct a hypothesis test.