Question

3. In the 1980s, it was generally believed that congenital abnormalities affected about 5% of the 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. A recent study examined 384 children and found that 46 of them showed signs of an abnormality. Is this strong evidence that the risk has increased?

a) Write the appropriate hypotheses.

b) Perform the test. What is the P-value?

c) Explain what the p-value means in this context.

Please show all work.

Typed work only, no Handwriting.

Answer 1

Q.3) Given that, n = 384 and x = 46

sample proportion = 46/384 = 0.1198

a) The null and the alternative hypotheses are,

H₀ : p = 0.05

H₁ : p > 0.05

b) Test statistic is,

Since, it is right-tailed test,

p-value = P(Z > 6.28) = 1 - P(Z < 6.28) = 1 - 1.0000 = 0.0000

=> p-value = 0.0000

c) Since, p-value is 0

We Reject the null hypothesis ( H₀) at any level of significance.

Therefore, we can conclude that, there is strong evidence that the risk has increased.