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 356 randomly selected children and found that 48 of them showed signs of an abnormality. Is this strong evidence that the risk has​ increased? (Consider a​ P-value of around 0.05 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. ​c) Perform the mechanics of the test. What is the test​ statistic? ​(Round to two decimal places as​ needed.) What is the​ 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 actual percentage of children who have genetic abnormalities.

B.The​ P-value is the chance of observing 48 or more children with genetic abnormalities in a random sample of 356 children.

C.The​ P-value is the chance of observing 7​% of children with genetic abnormalities.

D.The​ P-value is the chance of observing 48 or more children with genetic abnormalities in a random sample of 356 children if 7% of children actually have genetic abnormalities.

​e) What's your​ conclusion?

A.Reject H0. There is not sufficient evidence that more than 7% of the​ nation's children have genetic abnormalities.

B.Fail to reject H0. There is not sufficient evidence that more than 7% of the​ nation's children have genetic abnormalities.

C.Fail to reject H0. There is sufficient evidence that more than 7% of the​ nation's children have genetic abnormalities.

D.Reject H0. There is sufficient evidence that more than 7% of the​ nation's children have genetic abnormalities.

​f) Do environmental chemicals cause congenital​ abnormalities?

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

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

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

Answer 1

b)here as np>5 and n(!-p)>5 ; sample is random therefore we can use normal approximation of binomial distribution

c)test statistic z=4.79

p value =0.0000

d)D.The​ P-value is the chance of observing 48 or more children with genetic abnormalities in a random sample of 356 children if 7% of children actually have genetic abnormalities.

e)D.Reject H0. There is sufficient evidence that more than 7% of the​ nation's children have genetic abnormalities.

f)

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