Question

It 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. A recent study examined 374 randomly selected children and found that 47 of them showed signs of an abnormality. Is this strong evidence that the risk has increased?(Consider a P-value of around 5 % to represent reasonable evidence.)

Complete parts a through f.

a) Write appropriate hypotheses. Let p be the proportion of children with genetic abnormalities. Choose the correct answer below.

A. H0 : p = 0.08 vs. HA : p not = 0.08

B. H0 : p = 0.1257 vs. HA : p > 0.1257

C. H0 : p = 0.1257 vs. HA : p < 0.1257

D. H0 : p = 0.08 vs. HA : p < 0.08

E. H0 : p = 0.08 vs. HA : p > 0.08

F. H0 : p = 0.1257 vs. HA : p not = 0.1257

b) Check the necessary assumptions. Which of the following are satisfied? Select all that apply.

A. The sample is random.

B. Less than 10% of the population was sampled.

C. The data are independent.

D. There are more than 10 successes and 10 failures.

c) Perform the mechanics of the test. What is the test statistic?

z= ...... (Round to two decimal places as needed.)

What is the P-value?

P-value = ..... (Round to three decimal places as needed.)

d) Explain what the P-value means in this context. Choose the correct answer below.

A. The P-value is the chance of observing 8 % of children with genetic abnormalities.

B. The P-value is the chance of observing 47 or more children with genetic abnormalities in a random sample of 374 children if 8 % of children actually have genetic abnormalities.

C. The P-value is the chance of observing 47 or more children with genetic abnormalities in a random sample of 374

children.

D. The P-value is the actual percentage of children who have genetic abnormalities.

e) What's your conclusion?

A. Fail to reject H0. There is not sufficient evidence that more than 8% of the nation's children have genetic abnormalities.

B. Reject H0. There is not sufficient evidence that more than 8 % of the nation's children have genetic abnormalities.

C. Fail to reject H0. There is sufficient evidence that more than 8 % of the nation's children have genetic abnormalities.

D. Reject H0. There is sufficient evidence that more than 8 % of the nation's children have genetic abnormalities.

f) Do environmental chemicals cause congenital abnormalities?

A. No, the conclusion of the hypothesis test shows that environmental chemicals do not cause genetic abnormalities.

B. Yes, the conclusion of the hypothesis test shows that environmental chemicals cause genetic abnormalities.

C. It is unknown if environmental chemicals cause genetic abnormalities, because the hypothesis test does not indicate the cause of any changes.

Answer 1

Ans:

a)

H₀ : p = 0.08 vs. H_A : p > 0.08

b)A,C,D are correct.

c)

sample proportion=47/374=0.1257

Test statistic:

z=(0.1257-0.08)/SQRT(0.08*(1-0.08)/374)

z=3.26

p-value=P(z>3.26)=0.001

d)

The P-value is the chance of observing 47 or more children with genetic abnormalities in a random sample of 374 children if 8 % of children actually have genetic abnormalities.

e)It is unknown if environmental chemicals cause genetic abnormalities, because the hypothesis test does not indicate the cause of any changes.

Reject H₀. There is sufficient evidence that more than 8 % of the nation's children have genetic abnormalities.

f)