Question

in the 1980s, it was generally believed that congenital abnormalities affected about 8% of a large nation’s children. some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. is this strong evidence that the risk has increased? (we consider a p - value of around 5% to represent reasonable evidence.) complete parts a through f. assume the independence assumption is met.
e) whats your conclusion?
a. fail to reject ( h_0 ). there is sufficient evidence that more than 8% of the nation’s children have genetic abnormalities.
b. reject ( h_0 ). there is sufficient evidence that more than 8% of the nation’s children have genetic abnormalities.
c. reject ( h_0 ). there is not sufficient evidence that more than 8% of the nation’s children have genetic abnormalities.
d. fail to reject ( h_0 ). there is not sufficient evidence that more than 8% of the nation’s children have genetic abnormalities.
f) do environmental chemicals cause congenital abnormalities?
a. yes, the conclusion of the hypothesis test shows that environmental chemicals cause genetic abnormalities.
b. it is unknown if environmental chemicals cause genetic abnormalities, because the hypothesis test does not indicate the cause of any changes.
c. no, the conclusion of the hypothesis test shows that environmental chemicals do not cause genetic abnormalities.

Explanation:

Step1: State hypotheses

Let $p$ = proportion of children with abnormalities.
$H_0: p = 0.08$
$H_a: p > 0.08$

Step2: Calculate sample proportion

$\hat{p} = \frac{40}{373} \approx 0.1072$

Step3: Compare p-value to significance level

Given p-value ≈ 0.05, use $\alpha = 0.05$. Since $0.05 = 0.05$, reject $H_0$.

Step4: Interpret causal link

Hypothesis tests only show association, not causation.

Answer:

e) B. Reject $H_0$. There is sufficient evidence that more than 8% of the nation's children have genetic abnormalities.
f) B. It is unknown if environmental chemicals cause genetic abnormalities, because the hypothesis test does not indicate the cause of any changes.