Researchers studying the effects of diet on growth would like to know if a vegetarian diet affects the height of a child. The researchers randomly select 12 vegetarian children that are six years old. The average height of the children is 42.5 inches with a standard deviation of 3.8 inches. The average height for all six-year-old children is 45.75 inches. Conduct a hypothesis test to determine whether there is overwhelming evidence at a 0.05 level of significance that six-year-old vegetarian children are not the same height as other six-year-old children? Use the Rejection Region method.