Answer to Question #11516 in Statistics and Probability for M Marquis

Question

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 36 vegetarian children that are six years old. The average height of the children is 43.5 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 evidence at α=.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. (When answering this question, please state the null and alternative hypotheses, what the researchers are claiming, the p value, and your response to the question, ie compare the p value to α and decided whether or not to reject the null hypothesis and then answer the question.)