Exercise B.38 on page 314 describes a randomized trial in South Africa to test whether the proportion of babies born with infections is smaller if women in labor are treated with a wipe containing chlorohexidine rather than a sterile wipe (the placebo). A sample of n = 481 pregnant women were randomly split into the two groups. One goal of the study is to test H₀: p_c = p_w vs H_a: p_c < p_w, where p_c and pw are the proportion of babies who develop infections during childbirth with the respective treatments.

(a) What does it mean to make a Type I error in this situation?

(b) What does it mean to make a Type II error in this situation?

(c) In which of the following two situations should we select a smaller significance level:

• The drug chlorohexidine is very safe and known to have very few side effects.

• The drug chlorohexidine is relatively new and may have potentially harmful side effects for the mother and newborn child.

(d) The p-value for the data in this study is 0.32. What is the conclusion of the test?

(e) Does this conclusion mean that the treated wipes do not help prevent infections? Explain.  

Exercise B.38 on page 314

The Centers for Disease Control and Prevention (CDC) conducted a randomized trial in South Africa designed to test the effectiveness of an inexpensive wipe to be used during childbirth to prevent infections. Half of the mothers were randomly assigned to have their birth canal wiped with a wipe treated with a drug called chlorohexidine before giving birth, and the other half to get wiped with a sterile wipe (a placebo). The response variable is whether or not the newborns develop an infection. The CDC hopes to find out whether there is evidence that babies delivered by the women getting the treated wipe are less likely to develop an infection.