Question

It the? 1980s, it was generally believed that congenital abnormalities affected about 7?% 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 423 randomly selected children and found that 43 of them showed signs of an abnormality. 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.

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

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

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

BThe data are independent.

C.The sample is random.

D.Less than? 10% of the population was sampled.

c. Compute the test statistic.

z=___

?(Round to two decimal places as? needed.)

find the P value

P=_____

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

A.The? P-value is the chance of observing4343or more children with genetic abnormalities in a random sample of423423children.

B.The? P-value is the chance of observing77?%of children with genetic abnormalities.

C.The? P-value is the chance of observing4343or more children with genetic abnormalities in a random sample of423423children if77?%of children actually have genetic abnormalities.

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

?e) What's your? conclusion?

A.RejectRejectH0.Thereisissufficient evidence that more than77?%of the? nation's children have genetic abnormalities.

B.Fail to rejectFail to rejectH0.Thereis notis notsufficient evidence that more than77?%of the? nation's children have genetic abnormalities.

CFail to rejectFail to rejectH0.

Thereisissufficient evidence that more than77?%of the? nation's children have genetic abnormalities.

D.RejectRejectH0.Thereis notis notsufficient evidence that more than77?%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 It is unknown if environmental chemicals cause genetic? abnormalities, because the hypothesis test does not indicate the cause of any changes.

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

Answer 1

a) Null Hypothesis H0: p = 0.07

Alternative Hypothesis H1: p> 0.07

b) The necessary suumptions are

np = 423*0.07 = 29.61>10 and

nq = 423*0.93= 393.39> 10

Therefore,

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

BThe data are independent.

C.The sample is random.

c) Under H0, the test statistic is

$Z = \frac{\widehat{p} -p}{\sqrt{pq/n}} = \frac{0.10-0.07}{\sqrt{0.07*0.93/423}}=2.418$

d) The P-Value is 0.0078

A.The? P-value is the chance of observing 43or more children with genetic abnormalities in a random sample of 423 children.

e) Conclusion : A.RejectH0.There is sufficient evidence that more than 7?%of the? nation's children have genetic abnormalities.

f) C.?Yes, the conclusion of the hypothesis test shows that environmental chemicals cause genetic abnormalities.