9.19 Testing a headache remedy Studies that compare treatments for chronic medical conditions such as headaches can use the same subjects for each treatment. This type of study is commonly referred to as a crossover design.

With a crossover design, each person crosses over from using one treatment to another during the study. One such study considered a drug (a pill called Sumatriptan)

for treating migraine headaches in a convenience sample of children.6 The study observed each of 30 children at two times when he or she had a migraine headache. The child received the drug at one time and a placebo at the other time. The order of treatment was randomized and the study was double-blind. For each child, the response was whether the drug or the placebo provided better pain relief. Let p denote the proportion of children having better pain relief with the drug in the population of children who suffer periodically from migraine headaches. Can you conclude that p is different from 0.5, that is, either more or less than half of the population is getting better pain relief with the drug? Of the 30 children, 22 had more pain relief with the drug and 8 had more pain relief with the placebo.

a. For testing H0: p = 0.50 against Ha: p • 0.50, show that the test statistic z = 2.56.

b. Show that the P-value is 0.01. Interpret.

c. Check the assumptions needed for this test and discuss the limitations due to using a convenience sample rather than a random sample.