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In: Statistics and Probability

It the​ 1980s, it was generally believed that congenital abnormalities affected about 7​% of a large​...

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 409 randomly selected children and found that 58 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. Assume the independence assumption is met.

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

A.H0​: p=0.1418 vs. HA​: p>0.1418   B.H0​:p=0.1418 vs. HA​: p≠0.1418

C.H0​: p=0.1418 vs. HA​: p<0.1418 D.H0​:p=0.07 vs. HA​: p>0.07

E.H0​: p=0.07 vs. HA​: p<0.07   F. H0​: p=0.07 vs. HA​: p≠0.07

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

A.Less than​ 10% of the population was sampled.

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

C.The independence assumption is satisfied.

D.The sample is random.

c) Perform the mechanics of the test. What is the​ P-value?

​P-value=

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

A.The​ P-value is the chance of observing 58 or more children with genetic abnormalities in a random sample of 409 children.

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

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

D.The​ P-value is the chance of observing 58 or more children with genetic abnormalities in a random sample of 409 children if 7​%of children actually have genetic abnormalities.

​e) What's your​ conclusion?

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

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

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

D.Reject H0.There is not is not sufficient evidence that more than 7​% 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.

Solutions

Expert Solution

orchestra answered 1 year ago
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