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.
b) the result is statistically significant, but is it important? comment.
○ a. we concluded that the actual percentage of vaccinated children is below 90.9%. a 1.3% drop would probably not be considered noteworthy but in context, if 1,000,000 children are vaccinated each year a 1.3% difference accounts for 13000 more children not being vaccinated, which is important.
○ b. a 1.3% difference in child vaccinations in not important.
○ c. we conclude that the actual percentage of vaccinated children is below 90.9% and is about 89.6%. this drop is not important because only a 5% change or more can be considered important.
○ d. all statistically significant results are important.

Explanation:

• Option A: The P - value of \(P = 0.032\) (less than the common significance level of \(0.05\)) means we reject the null hypothesis. So, we conclude the actual vaccination rate is below \(90.9\%\). A \(1.3\%\) drop (\(90.9\% - 89.6\%\)) may seem small in percentage terms. But when scaled up (e.g., for \(1,000,000\) children, \(1.3\%\) of \(1,000,000=13000\) children), it has real - world implications for public health.
• Option B: Ignores the potential large - scale impact of the percentage difference.
• Option C: Arbitrarily sets \(5\%\) as the threshold for importance without considering context.
• Option D: Incorrect as statistical significance (based on probability) does not always equate to practical importance.

Answer:

A. We concluded that the actual percentage of vaccinated children is below 90.9%. A 1.3% drop would probably not be considered noteworthy but in context, if 1,000,000 children are vaccinated each year a 1.3% difference accounts for 13000 more children not being vaccinated, which is important.