Question

In the 1990s, it was generally believed that genetic abnormalities affected about 9% 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, which could have important implications for health insurance companies. A recent study examined 385 randomly selected children and found that 43 of them showed signs of a genetic abnormality.

(a) Which hypotheses should be used to test if the proportion of genetic abnormalities has increased in recent years?

H₀: p = 0.09 vs. H_a: p > 0.09

H₀: p = 0.1117 vs. H_a: p < 0.1117   

H₀: p = 0.1117 vs. H_a: p ≠ 0.1117

H₀: p = 0.09 vs. H_a: p ≠ 0.09

H₀: p = 0.09 vs. H_a: p < 0.09

H₀: p = 0.1117 vs. H_a: p > 0.1117

(b) Are the conditions met for doing the hypothesis test?

The 15 successes and failures condition is met.

None of the conditions are met.

The sample was randomly chosen.

The children taking part in the study were independent of each other.

(c) What is the p-value? (Use 3 decimals.)

(d) What does this p-value mean?

The p-value is the chance of observing 43 or more children with genetic abnormalities in a random sample of 385 children, if the true proportion of children with genetic abnormalities is 11.17%.

The p-value is the chance of observing 43 or more children with genetic abnormalities in a random sample of 385 children, if the true proportion of children with genetic abnormalities is 9%.    

The p-value is the chance of observing 9% of children with genetic abnormalities.

The p-value gives the actual percentage of children who have genetic abnormalities.

(e) What is the conclusion of the hypothesis test, for α = 0.05?

Reject H₀. There is insufficient evidence that more than 9% of this nation's children have genetic abnormalities.

Do not reject H₀. There is sufficient evidence that more than 9% of this nation's children have genetic abnormalities.    

Reject H₀. There is sufficient evidence that more than 9% of this nation's children have genetic abnormalities.

Do not reject H₀. There is insufficient evidence that more than 9% of this nation's children have genetic abnormalities.

(f) Do this study show that environmental chemicals cause congenital abnormalities?

Yes, the hypothesis test shows that environmental chemicals cause the genetic abnormality.

No, the hypothesis test shows that environmental chemicals do not cause the genetic abnormality.    

This study does not address what causes the genetic abnormality.

Answer 1

Part a)

H₀: p = 0.09 vs. H_a: p > 0.09

Part b)

The sample was randomly chosen.

Part d)

The p-value is the chance of observing 43 or more children with genetic abnormalities in a random sample of 385 children, if the true proportion of children with genetic abnormalities is 9%.    

Part e)

P = X / n = 43/385 = 0.1117

Test Statistic :-
Z = ( P - P0 ) / √ ((P0 * q0)/n))
Z = ( 0.111688 - 0.09 ) / √(( 0.09 * 0.91) /385))
Z = 1.487

Decision based on P value
P value = P ( Z > 1.487 ) =  P value = 0.0685
Reject null hypothesis if P value < α = 0.05
Since P value = 0.0685 > 0.05, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Part f)

No, the hypothesis test shows that environmental chemicals do not cause the genetic abnormality.