Question

Public health officials believe that 91​% 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 88.1​% had been vaccinated. A statistician would reject the​ 98% hypothesis with a​ P-value of P= 0.0001.
Required:
a. Explain what the P-value means in this context.
b. The result is statistically significant, but is it important?

Answer 1

Answer:

a) The p value is a probability always between 0 and 1 and represent the evidence in favor of the alternative hypothesis if it's a low value then we have enough evidence to reject the null hypothesis otherwise we FAIl to reject the null hypothesis

b) For this case the result is important because the parameter established by the Public Healt is incorrect ,we obtain a significant result so then there is enough evidence to conclude that the true proportion of children that have been vaccinated against measles is lower than 91%

Step-by-step explanation:

For this case the system of hypothesis are:

Null hypothesis:$p=0.91$  

Alternative hypothesis:$p < 0.91$  

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)  

For this case after conduct the hypothesis we have the following p value obtained:

$p_v = 0.0001$

Part a

The p value is a probability always between 0 and 1 and represent the evidence in favor of the alternative hypothesis if it's a low value then we have enough evidence to reject the null hypothesis otherwise we FAIl to reject the null hypothesis

Part b

For this case the result is important because the parameter established by the Public Healt is incorrect ,we obtain a significant result so then there is enough evidence to conclude that the true proportion of children that have been vaccinated against measles is lower than 91%