Question 1: # The mean weight of all 20 year-old-women is 128 pounds (www.kidsgrowth.com). # Suppose the population weights of 20 year old women are normally distributed.

# A random sample of 40 vegetarian women who are 20 years old showed a sample mean of 122 pounds # with a standard deviation 15 pounds.

# Is there enough evidence to conclude that the average 20-year old vegetarian woman weighs less than the average 20-year old woman?

(a) Why is it okay to use a t-procedure in this situation? State the hypotheses of the test. (b) Calculate the test-statistic by hand. (c) Find the p-value of the test. Show R code and output. (d) Interpret the p-value. (e) State the conclusion of the test.