Question

public health officials believe that 90.9% of children have been vaccinated against measles. a random survey of medical records at many schools across the country found that, among more than 13,000 children, only 89.6% had been vaccinated. a statistician would reject the 90% hypothesis with a p - value of p = 0.032.
a) explain what the p - value means in this context.
b) the result is statistically significant, but is it important? comment.
a) explain what the p - value means in this context.
○ a. there is only a 3.2% chance that 90.9% is the actual percentage of vaccinated children.
○ b. there is only a 3.2% chance of seeing a sample proportion as low as 89.6% vaccinated by natural sampling variation if 90.9% have really been vaccinated.
○ c. there is only a 3.2% chance that 90.9% is not the actual percentage of children vaccinated.
○ d. there is only a 3.2% chance that a sample proportion of 89.6% is statistically different from the reported 90.9% of children vaccinated.

Explanation:

The P - value is the probability of obtaining a result as extreme or more extreme than the observed result, assuming the null hypothesis is true. In this case, the null hypothesis is that the proportion of vaccinated children is \(p = 0.909\).

Answer:

B. There is only a 3.2% chance of seeing a sample proportion as low as 89.6% vaccinated by natural sampling variation if 90.9% have really been vaccinated.