question1

(1) Confidence intervals and tests of significance are two most common types of statistical inference. You are required to explain in a few sentences the fundamental differences between these two types of statistical inference by giving relevant examples when one type of statistical inference method is preferred over the other. (ii) Nutritionists believe that a vegetarian diet has no effect on the height of children. A group of researchers in China 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 300 vegetarian children in China who are five years old. The average height of these children was found to be 44.5 inches with a standard deviation of 3.8 inches. The average height for all five-year-old children in China is known to be 45.75 inches. Conduct a hypothesis test to determine whether there is overwhelming evidence at a=.05 that five-year-old vegetarian children are not the same height as other five-year-old children in China. Assume that the height of a five-year-old vegetarian child in China is approximately normally distributed