Sparked by recent controversy, researchers wanted to study if there is a relationship between receiving a certain vaccine and developing signs of autism. For 800 children, the researchers tallied whether or not a child received the vaccine and also whether the child developed no signs of autism or some signs of autism. There were 300 children who did not receive the vaccine and 500 children who did. Of the 300 children who did not receive the vaccine, 12 showed signs of autism. Of the 500 children who did receive the vaccine, 16 showed signs of autism. Test whether the population proportion of all children who developed signs of autism is different among those who did and did not receive the vaccine. In other words, if p1 is the population proportion of all unvaccinated children who develop signs of autism and p2 is the population proportion of all vaccinated children who develop signs of autism; we want to test H0: p1 = p2 versus Ha: p1 ≠ p2 at a 1% level.
a. Compute the test statistic needed to perform the test.
b. Upload a complete sketch of the p-value.
c. Report the value of the p-value.
d. A reporter from a news agency wants the statistical report translated into a simple sentence about the effect of the vaccine on autism. Provide that simple sentence.