Researchers studying the effect of diet on growth would like to know if a vegetarian diet affects the height of a child. Twelve students are randomly selected that are all 6-years old. The average height of these kids is 42.5 inches with a standard deviation of 3.8 inches. The average height of all 6-year old kids is found to be 45.75 inches. Conduct a hypothesis test to determine if there is overwhelming evidence at alpha = .05 that 6-year old vegetarian kids are not the same height as other six year-old kids. Determine the critical values, test statistic and any specific information from the problem.