A study of iron deficiency among infants compared blood hemoglobin levels of a random sample of infants who had been breast-fed to a random sample of infants who had been fed with standard infant formula. Here
are the results.

n x s
Breast-fed infants 23 13.3 1.7
Formula-fed infants 19 12.4 1.8

We want to test 0 : 0 H μ μ B F − = , : 0 HaB F μ μ − ≠ , where μ B and μ F are the population mean blood
hemoglobin levels for breast-fed and formula-fed infants, respectively.
(a) What additional information would you need to confirm that the conditions for this test have been met?

(b) Assume the conditions have been met. Calculate the standardized test statistic and P-value for this test.

(c) What conclusion would you make at the α = 0.05 significance level?

(d) Given your conclusion in part (c), which type of error, Type I or Type II, could you have made?
Describe that error in the context of this study.