Chapter 21, Problem 7E

(a)

To determine

To explain what the P-value means in this context.

Explanation of Solution

It is given in the question that public health official believe that $90\%$ of children have been vaccinated against measles. A random survey of medical records at many schools across the country found that, among more than $13000$ children, only $89.4\%$ had been vaccinated. A statistician would reject the $90\%$ hypothesis with a P-value of $P=0.011$ . Thus, the P-value means in this context that there is a $1.1\%$ chance that there will be a sample proportion as low as $89.4\%$ vaccinated by natural sampling variation alone if $90\%$ have been vaccinated.

(b)

To determine

To comment on the statement.

Explanation of Solution

It is given in the question that public health official believe that $90\%$ of children have been vaccinated against measles. A random survey of medical records at many schools across the country found that, among more than $13000$ children, only $89.4\%$ had been vaccinated. A statistician would reject the $90\%$ hypothesis with a P-value of $P=0.011$ . Thus, we concluded that p is below $0.9$ , but a $95\%$ confidence interval would show that the true proportion is between $(0.889,0.899)$ . A decrease from $90\%\text{ to 89}\text{.9\%}$ would most likely not to be considered very significant.