The birth weight for babies is normally distributed with a mean of 7.5 lb and a standard deviation of 1.125 lb. Suppose a pediatrician claims that the average birth weight for babies under her care is greater than 7.5 lb. She randomly selects 30 newborns and produces an average birth weight of 8 lb. Which of the following is true if the pediatrician uses a p-value approach to implement a hypothesis test at a 5% significance level to support her claim?
A) The null hypothesis is H0: µ = 7.5.
B) A two-tailed hypothesis test should be used.
C) The allowed probability of making a Type II error is 5%.
D) The p-value = p( X−X− ≥ 7.5) = P(Z ≥ 2.434) = 0.0075