2. Suppose that it is known from a national survey that the length of newborns (cm)

follows a normal distribution with μ=50. Answer the following questions.

(a) If you repeatedly draw samples from this population with a fixed sample of size, where should the sampling distribution of the sample means be centered around? Why?

(b) Suppose that you are interested in whether maternal anemia has an impact on the length of newborns and randomly draw 50 newborns whose mothers have anemia; the sample x = 45, s = 3. State your hypothesis and perform two-sided significance tests at significance level  =0.05.