A randomized experimental study was conducted to evaluate the effectiveness of a new pertussis vaccine. One-thousand healthy children were randomized to receive either the new vaccine (500 children) or the old vaccine (500 children). The children were followed for two years to monitor the incidence of pertussis. At the end of the study, the risk ratio for developing pertussis was 0.5 among the children who received the new vaccine compared to children who received the old vaccine. The 95% confidence interval for this relative risk was 0.2-0.8 and the p value was 0.01. Which of the following is the correct interpretation of the p-value?

a. Children who received the new vaccine had a 50% reduced risk (or half the risk) of developing pertussis compared to those who received the old vaccine.

b. Given that the null hypothesis is true, there is a 1% probability of observing these or more extreme results.

c. I have 95% confidence that the true relative risk lies in the interval from 0.2 to 0.8.

d. The number of excess cases of pertussis among those who received the old vaccine is 10 per 1000.

After establishing the null and alternative hypotheses and then calculating a probability statistic to determine if the study results are compatible with the null hypothesis, the next step is to

a. Describe the person, place, and time characteristics of the disease to generate hypotheses

b. Calculate measures of disease frequency to generate hypotheses

c. Select a random sample from the study population

d. Decide whether to reject or not to reject the null hypothesis according to the degree of compatibility with the null hypothesis

To test a hypothesis, the first step is to establish null and alternative hypotheses. The next step is to

a. Describe the person, place, and time characteristics of the disease to generate hypotheses

b. Calculate measures of disease frequency to generate hypotheses

c. Use a probability statistic or method to determine the compatibility of the study results with the null hypothesis

d. Decide whether to reject or not to reject the null hypothesis according to the degree of compatibility with the null hypothesis

Which of the following are sources of random error in epidemiological studies?

a. Selection of an unrepresentative sample of the population just by chance and mistakes in assessing the exposure and disease

b. A mixing of effects between an exposure, an outcome, and a third extraneous variable

c. An effect that results in the strength of the association between an exposure and a disease being different according to the level of another variable.

d. None of the above