Question: Testing a headache remedy: Studies that compare treatments for chronic medical conditions such as headaches can use the same subjects for each treatment. With a crossover design, each person crosses over from using one treatment to another during the study. One such study considered a drug for treating migraine headaches in a convenience sample of children. The study observed 30 children at 2 times when he or she had a migraine. The child received the drug at one tiMeand a placebo at the other. The order was random and was a blind-study. For each child, the response was whether the drug or the placebo provided better pain relief. Let P donate the proportion of children having better pain relief with the drug. Can you conclude that P>0.50, more than half of the population is getting better with the drug, or vice versa? Of the 30 children, 22 had more pain relief with the drug and 8 had more pain relief with the placebo.

a. For testing Ho: p = 0.50 against Ha: p doesn’t not = 0.50, show that the test statistic z =2.56

b. Show that P-value is 0.0104 and interpret.

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