Problem 1

  1. False. The number of patients with cardiovascular problems is not what is important, the percentage of patients is.

  2. True.

  3. False. The reasoning is wrong; the rate of incedence alone is not enough to prove anything.

  4. True.

Problem 2

  1. In the treatment group, the proportion of patients who died is \(\frac{45}{69} = 0.652\). In the control group, the proportion of patients who died is \(\frac{30}{34} = 0.882\).
  2. i.$H_0 = $ the treatment does not affect the rate of death of patients. \(H_A=\) the treatment affects the rate of death of patients.

  1. Blanks are as follows: 28, 75, 69, 34, “The mean of the difference in proportions”, “as extreme or more extreme as the observed rate of occurrence.”

  2. We can reject the null hypothesis, since only about two percent of the simulated differences are more extreme that our observed difference.

Problem 3.

  1. This is an experiment.

  2. Yes, since the control group recieved placebo treatment.

  3. \((66/85) - (65/81) = -0.026\)

  4. At first glance, placebo is better, since it has a higher rate of self reported improvement.

  5. $H_0 = $ the antibiotic has no effect on improvement in symptoms.

$H_A = $ the antibiotic has an effect on improvement in symptoms.

  1. We can conclude that we cannot reject the null hypothesis. The value observed in the study is not above the mean value observed in the simulations, let alone a statistically significant amount above the mean.