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 selected 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 that six year old vegetarian children are not the same height as other six year old children. Assume that the heights of six year old vegetarian children are approximately normally distributed.

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